A261898 - OEIS

%I #13 Feb 28 2017 10:24:25

%S 1,1,4,25,210,2205,27720,405405,6756750,126351225,2618916300,

%T 59580345825,1475759335050,39529267903125,1138442915610000,

%U 35078272337233125,1151392703775063750,40106845848164720625,1477620636511331812500,57405561728465240915625

%N Values of |G-hat_1(n)|, a sum involving Stirling numbers of the second kind.

%H Alois P. Heinz, <a href="/A261898/b261898.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)))(-1):

%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}]][-1]; 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