A261899 Values of |G-hat_2(n)|, a sum involving Stirling numbers of the second kind.

1, 1, 5, 36, 340, 3955, 54495, 866250, 15585570, 312837525, 6926344425, 167610643200, 4399779384000, 124490841049575, 3776362727011875, 122240308063623750, 4205265824898888750, 153199195863404315625, 5891484566433038698125, 238487970732928954537500

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

H. W. Gould, Harris Kwong, Jocelyn Quaintance, On Certain Sums of Stirling Numbers with Binomial Coefficients, J. Integer Sequences, 18 (2015), #15.9.6.

Maple

a:= n-> (m-> abs(add((-1)^k*binomial(2*n+m, n-k)
         *combinat[stirling2](n+k, k), k=0..n)))(-2):
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}]][-2]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 28 2017, after Alois P. Heinz *)

Crossrefs

Sequence in context: A141764 A075744 A277610 * A109186 A099391 A008785

Adjacent sequences: A261896 A261897 A261898 * A261900 A261901 A261902

Keyword

nonn

Author

N. J. A. Sloane, Sep 06 2015

Extensions

More terms from Alois P. Heinz, Sep 06 2015

Status

approved