Revisions by Paolo Xausa
(See also Paolo Xausa's wiki page)
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#16 by Paolo Xausa at Fri Aug 30 16:22:25 EDT 2024
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#13 by Paolo Xausa at Fri Aug 30 16:22:07 EDT 2024
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#8 by Paolo Xausa at Fri Aug 30 16:21:26 EDT 2024
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#7 by Paolo Xausa at Fri Aug 30 16:20:57 EDT 2024
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| FORMULA
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T(n, k) = numerator((n+1))*binomial(n, k)/binomial(2n, n)).
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#6 by Paolo Xausa at Fri Aug 30 16:19:44 EDT 2024
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Paolo Xausa, <a href="/A098505/b098505_1.txt">Table of n, a(n) for n = 0..11475</a> (rows 0..150 of triangle, flattened).
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| FORMULA
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Triangle T(n, k)=) = numerator((n+1)binomial(n, k)/binomial(2n, n)))).
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| EXAMPLE
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Rows begin:
1;
1,1;
1,1,1;
1,3,3,1;
1,2,3,2,1;
1,5,5,5,5,1;
...
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| MATHEMATICA
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Table[Numerator[(n + 1)*Binomial[n, k]/Binomial[2*n, n]], {n, 0, 15}, {k, 0, n}] (* Paolo Xausa, Aug 30 2024 *)
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| CROSSREFS
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Cf. A098474, A098506, A098507, A098508, A093527.
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| STATUS
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approved
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#12 by Paolo Xausa at Fri Aug 30 16:13:39 EDT 2024
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Paolo Xausa, <a href="/A098508/b098508_1.txt">Table of n, a(n) for n = 0..10000</a>
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| MATHEMATICA
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Table[Numerator[n*(n^2 - 1)/(2*Binomial[2*n, n])], {n, 0, 100}] (* Paolo Xausa, Aug 30 2024 *)
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approved
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#15 by Paolo Xausa at Fri Aug 30 11:17:49 EDT 2024
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Paolo Xausa, <a href="/A230078/b230078_1.txt">Table of n, a(n) for n = 1..10000</a>
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| MATHEMATICA
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With[{upto = 100}, Complement[Range[upto], 2*Join[{1}, Select[Range[upto/2], PrimePowerQ]]]] (* Paolo Xausa, Aug 30 2024 *)
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| CROSSREFS
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Cf. A138929 (complement), 2*A020513, A230079 (1/rho(a(n))) .))).
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approved
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#15 by Paolo Xausa at Fri Aug 30 04:35:54 EDT 2024
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#32 by Paolo Xausa at Fri Aug 30 04:35:44 EDT 2024
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#15 by Paolo Xausa at Fri Aug 30 04:35:39 EDT 2024
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