A261901 - OEIS

%I #17 Mar 01 2022 08:15:27

%S 1,1,7,61,679,9150,144186,2594410,52390030,1171745575,28726923225,

%T 765549820035,22022976400425,679930906554900,22417065396425700,

%U 785869955615745000,29184350973268491000,1144300243940081353125,47232865043365173046875,2047016588845893645605625

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

%H Alois P. Heinz, <a href="/A261901/b261901.txt">Table of n, a(n) for n = 0..400</a>

%H H. W. Gould, Harris Kwong, and 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              *Stirling2(n+k, k), k=0..n)))(-4):

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

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

%t     StirlingS2[n + k, k], {k, 0, n}]]];

%t Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Mar 01 2022, after _Alois P. Heinz_ *)

%Y Cf. A048993 (Stirling numbers of 2nd kind).

%K nonn

%O 0,3

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

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