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Values of |F-hat_4(n)|, a sum involving Stirling numbers of the second kind.
1

%I #7 Sep 06 2015 17:35:16

%S 0,0,0,0,0,1,119,6825,302995,12122110,466876410,17892864990,

%T 694740296250,27610143335775,1129764045234825,47758910109285375,

%U 2089664150235787125,94720506100682962500,4449180413533177822500,216538502534948561467500,10915617077295918089602500

%N Values of |F-hat_4(n)|, a sum involving Stirling numbers of the second kind.

%H Alois P. Heinz, <a href="/A261686/b261686.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+m)))(-4):

%p seq(a(n), n=0..20); # _Alois P. Heinz_, Sep 06 2015

%K nonn

%O 0,7

%A _N. J. A. Sloane_, Sep 06 2015

%E More terms from _Alois P. Heinz_, Sep 06 2015