A261689 Values of g-hat_4(n), a sum involving Stirling numbers of the first kind.

1, 1, 11, 131, 1821, 29121, 526631, 10619735, 236128585, 5736575845, 151132416435, 4290611159835, 130556978677125, 4238232623249625, 146189527883974575, 5338862100892695375, 205783734992407196625, 8347924728847446868125, 355508623895766152686875

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-> add((-1)^k*binomial(2*n+m, n-k)
         *combinat[stirling1](n+k, k), k=0..n))(-4):
seq(a(n), n=0..20);  # Alois P. Heinz, Sep 06 2015

Mathematica

a[n_] := Function[m, Sum[(-1)^k*Binomial[2n+m, n-k]*StirlingS1[n+k, k], {k, 0, n}]][-4]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 28 2017, after Alois P. Heinz *)

Crossrefs

Sequence in context: A082148 A075509 A061113 * A101334 A222872 A068645

Adjacent sequences: A261686 A261687 A261688 * A261690 A261691 A261692

Keyword

nonn

Author

N. J. A. Sloane, Sep 06 2015

Extensions

More terms from Alois P. Heinz, Sep 06 2015

Status

approved