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A172111
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a(n) is the number of ordered partitions of {1, 1, 1, 1, 2, 3, ..., n-3}.
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2
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0, 0, 0, 8, 48, 368, 3408, 36848, 454608, 6294128, 96556368, 1624775408, 29744591568, 588384837488, 12503968334928, 284065406275568, 6869235761650128, 176150548586638448, 4774198652678411088
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OFFSET
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1,4
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COMMENTS
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a(n) is T_4(n) in the Griffiths and Mezo reference. - G. C. Greubel, Apr 15 2022
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LINKS
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FORMULA
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a(n) = Sum_{m=1..n} Sum_{j=0..m} binomial(m,j)*binomial(j+3,4)*(-1)^(m-j)*j^(n-4), for n>=4, with a(n) = 0 for n < 4.
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MATHEMATICA
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f[r_, n_]:= If[n<4, 0, Sum[Sum[Binomial[m, l]Binomial[l+r-1, r](-1)^(m-l)l^(n-r), {l, m}], {m, n}]]; Table[f[4, n], {n, 25}]
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PROG
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(Magma) [0, 0, 0] cat [(&+[ (&+[Binomial(k, j)*Binomial(j+3, 4)*(-1)^(k-j)*j^(n-4): j in [0..k]]): k in [1..n]]): n in [4..25]]; // G. C. Greubel, Apr 15 2022
(Sage) [0, 0, 0]+[sum(sum(binomial(k, j)*binomial(j+3, 4)*(-1)^(k+j)*j^(n-4) for j in (0..k)) for k in (1..n)) for n in (4..25)] # G. C. Greubel, Apr 15 2022
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CROSSREFS
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This gives the row sums of A172108.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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