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%I #13 Feb 28 2017 10:24:17
%S 1,1,5,36,340,3955,54495,866250,15585570,312837525,6926344425,
%T 167610643200,4399779384000,124490841049575,3776362727011875,
%U 122240308063623750,4205265824898888750,153199195863404315625,5891484566433038698125,238487970732928954537500
%N Values of |G-hat_2(n)|, a sum involving Stirling numbers of the second kind.
%H Alois P. Heinz, <a href="/A261899/b261899.txt">Table of n, a(n) for n = 0..400</a>
%H H. W. Gould, Harris Kwong, Jocelyn Quaintance, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Kwong/kwong9.html">On Certain Sums of Stirling Numbers with Binomial Coefficients</a>, J. Integer Sequences, 18 (2015), #15.9.6.
%p a:= n-> (m-> abs(add((-1)^k*binomial(2*n+m, n-k)
%p *combinat[stirling2](n+k, k), k=0..n)))(-2):
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Sep 06 2015
%t a[n_] := Function[m, Abs @ Sum[(-1)^k*Binomial[2n+m, n-k]*StirlingS2[n+k, k], {k, 0, n}]][-2]; Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Feb 28 2017, after _Alois P. Heinz_ *)
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Sep 06 2015
%E More terms from _Alois P. Heinz_, Sep 06 2015
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