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A261687
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Values of g-hat_2(n), a sum involving Stirling numbers of the first kind.
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1
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1, 1, 7, 61, 655, 8365, 123795, 2082465, 39234195, 818242425, 18711467775, 465512372325, 12516455726775, 361666448468325, 11176241678476875, 367788214424255625, 12840711103211866875, 474053962648722080625, 18451259976779359104375, 755138026289116122778125
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OFFSET
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0,3
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LINKS
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MAPLE
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a:= n-> (m-> add((-1)^k*binomial(2*n+m, n-k)
*combinat[stirling1](n+k, k), k=0..n))(-2):
# second Maple program:
a:= proc(n) option remember; `if`(n<2, 1, ((2*n-3)*
(4*n^3+9*n^2-n-3)*a(n-1))/(4*n^3-3*n^2-7*n+3))
end:
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MATHEMATICA
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a[n_] := Sum[(-1)^k Binomial[2n-2, n-k] StirlingS1[n+k, k], {k, 0, n}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 18 2017 *)
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PROG
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(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(2*n-2, n-k)*stirling(n+k, k, 1)); \\ Michel Marcus, Mar 18 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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