A261898 Values of |G-hat_1(n)|, a sum involving Stirling numbers of the second kind.

1, 1, 4, 25, 210, 2205, 27720, 405405, 6756750, 126351225, 2618916300, 59580345825, 1475759335050, 39529267903125, 1138442915610000, 35078272337233125, 1151392703775063750, 40106845848164720625, 1477620636511331812500, 57405561728465240915625

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)))(-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

Adjacent sequences: A261895 A261896 A261897 * A261899 A261900 A261901

Keyword

nonn

Author

N. J. A. Sloane, Sep 06 2015

Extensions

More terms from Alois P. Heinz, Sep 06 2015

Status

approved