A261687 Values of g-hat_2(n), a sum involving Stirling numbers of the first kind.

1, 1, 7, 61, 655, 8365, 123795, 2082465, 39234195, 818242425, 18711467775, 465512372325, 12516455726775, 361666448468325, 11176241678476875, 367788214424255625, 12840711103211866875, 474053962648722080625, 18451259976779359104375, 755138026289116122778125

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))(-2):
seq(a(n), n=0..20);  # Alois P. Heinz, Sep 06 2015
# second Maple program:
a:= proc(n) option remember; `if`(n<2, 1, ((2*n-3)*
      (4*n^3+9*n^2-n-3)*a(n-1))/(4*n^3-3*n^2-7*n+3))
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Sep 06 2015

Mathematica

a[n_] := Sum[(-1)^k Binomial[2n-2, n-k] StirlingS1[n+k, k], {k, 0, n}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 18 2017 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(2*n-2, n-k)*stirling(n+k, k, 1)); \\ Michel Marcus, Mar 18 2017

Crossrefs

Cf. A261898.

Sequence in context: A061634 A049402 A218498 * A001830 A213326 A261901

Adjacent sequences: A261684 A261685 A261686 * A261688 A261689 A261690

Keyword

nonn

Author

N. J. A. Sloane, Sep 06 2015

Extensions

More terms from Alois P. Heinz, Sep 06 2015

Status

approved