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A261687 Values of g-hat_2(n), a sum involving Stirling numbers of the first kind. 1
1, 1, 7, 61, 655, 8365, 123795, 2082465, 39234195, 818242425, 18711467775, 465512372325, 12516455726775, 361666448468325, 11176241678476875, 367788214424255625, 12840711103211866875, 474053962648722080625, 18451259976779359104375, 755138026289116122778125 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified July 8 01:48 EDT 2020. Contains 335502 sequences. (Running on oeis4.)