A261689 - OEIS

%I #13 Feb 28 2017 10:24:34

%S 1,1,11,131,1821,29121,526631,10619735,236128585,5736575845,

%T 151132416435,4290611159835,130556978677125,4238232623249625,

%U 146189527883974575,5338862100892695375,205783734992407196625,8347924728847446868125,355508623895766152686875

%N Values of g-hat_4(n), a sum involving Stirling numbers of the first kind.

%H Alois P. Heinz, <a href="/A261689/b261689.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-> add((-1)^k*binomial(2*n+m, n-k)

%p          *combinat[stirling1](n+k, k), k=0..n))(-4):

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

%t a[n_] := Function[m, Sum[(-1)^k*Binomial[2n+m, n-k]*StirlingS1[n+k, k], {k, 0, n}]][-4]; 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