A261901 Values of |G-hat_4(n)|, a sum involving Stirling numbers of the second kind.

1, 1, 7, 61, 679, 9150, 144186, 2594410, 52390030, 1171745575, 28726923225, 765549820035, 22022976400425, 679930906554900, 22417065396425700, 785869955615745000, 29184350973268491000, 1144300243940081353125, 47232865043365173046875, 2047016588845893645605625

Offset

0,3

Links

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

H. W. Gould, Harris Kwong, and 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)
             *Stirling2(n+k, k), k=0..n)))(-4):
seq(a(n), n=0..20);  # Alois P. Heinz, Sep 06 2015

Mathematica

a[n_] := With[{m = -4}, Abs[Sum[(-1)^k*Binomial[2*n + m, n - k]*
    StirlingS2[n + k, k], {k, 0, n}]]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 01 2022, after Alois P. Heinz *)

Crossrefs

Cf. A048993 (Stirling numbers of 2nd kind).

Sequence in context: A261687 A001830 A213326 * A368324 A350157 A048287

Adjacent sequences: A261898 A261899 A261900 * A261902 A261903 A261904

Keyword

nonn

Author

N. J. A. Sloane, Sep 06 2015

Extensions

More terms from Alois P. Heinz, Sep 06 2015

Status

approved