A261688 Values of g-hat_3(n), a sum involving Stirling numbers of the first kind.

1, 1, 9, 93, 1149, 16569, 273077, 5060825, 104129025, 2354517165, 58020227265, 1547299398645, 44393468444325, 1363355665697025, 44620110552142125, 1550263572136904625, 56983667551893707625, 2209245411411957043125, 90095221067259428645625

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))(-3):
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}]][-3]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 28 2017, after Alois P. Heinz *)

Crossrefs

Sequence in context: A181958 A082724 A061635 * A246212 A163951 A231658

Adjacent sequences: A261685 A261686 A261687 * A261689 A261690 A261691

Keyword

nonn

Author

N. J. A. Sloane, Sep 06 2015

Extensions

More terms from Alois P. Heinz, Sep 06 2015

Status

approved