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A084851
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Binomial transform of binomial(n+2,2).
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6
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1, 4, 13, 38, 104, 272, 688, 1696, 4096, 9728, 22784, 52736, 120832, 274432, 618496, 1384448, 3080192, 6815744, 15007744, 32899072, 71827456, 156237824, 338690048, 731906048, 1577058304, 3388997632, 7264534528, 15535702016, 33151778816
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: (1 - x)^2/(1 - 2*x)^3.
a(n) = (n^2 + 7*n + 8)*2^(n - 3).
a(n) = Sum_{k=0..n} C(n, k)*C(k+2, 2).
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EXAMPLE
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Let the triangle:
1
3, 4
6, 9, 13
10, 16, 25, 38
15, 25, 41, 66, 104
21, 36, 61, 102, 168, 272
28, 49, 85, 146, 248, 416, 688
36, 64, 113, 198, 344, 592, 1008, 1696, etc.
where the first column is A000217 (without 0). The other terms are calculated with the recurrence T(r, c) = T(r-1, c-1) + T(r, c-1).
The sequence is the right side of the triangle.
(End)
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MAPLE
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a := n -> hypergeom([-n, 3], [1], -1);
seq(round(evalf(a(n), 32)), n=0..31); # Peter Luschny, Aug 02 2014
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MATHEMATICA
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CoefficientList[ Series[(1 - x)^2/(1 - 2 x)^3, {x, 0, 28}], x] (* Robert G. Wilson v, Jun 28 2005 *)
LinearRecurrence[{6, -12, 8}, {1, 4, 13}, 30] (* Harvey P. Dale, Aug 05 2019 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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