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URL: https://oeis.org/A261898

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A261898
Values of |G-hat_1(n)|, a sum involving Stirling numbers of the second kind.
2
1, 1, 4, 25, 210, 2205, 27720, 405405, 6756750, 126351225, 2618916300, 59580345825, 1475759335050, 39529267903125, 1138442915610000, 35078272337233125, 1151392703775063750, 40106845848164720625, 1477620636511331812500, 57405561728465240915625
OFFSET
0,3
LINKS
H. W. Gould, Harris Kwong, and Jocelyn Quaintance, On Certain Sums of Stirling Numbers with Binomial Coefficients, J. Integer Sequences, 18 (2015), #15.9.6.
FORMULA
From Abdallah Daddi-Moussa-Ider, Aug 19 2025: (Start)
a(n) = n!*(n+2)*binomial(2*n,n)/(3*2^n) for n > 0.
a(n) = (1/3)*(n+2)*(2*n-1)!! for n > 0. (End)
MAPLE
a:= n-> (m-> abs(add((-1)^k*binomial(2*n+m, n-k)
*combinat[stirling2](n+k, k), k=0..n)))(-1):
seq(a(n), n=0..20); # Alois P. Heinz, Sep 06 2015
MATHEMATICA
a[n_] := Function[m, Abs @ Sum[(-1)^k*Binomial[2n+m, n-k]*StirlingS2[n+k, k], {k, 0, n}]][-1]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 28 2017, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A332257 A203219 A064299 * A038174 A049118 A305323
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 06 2015
EXTENSIONS
More terms from Alois P. Heinz, Sep 06 2015
STATUS
approved