cp's OEIS Frontend

A321963 Stieltjes generated from the sequence m, m+1, m+2, m+3, .... where m = 4.

%I A321963 #13 Jul 22 2019 02:43:43
%S A321963 1,4,36,444,6636,114084,2194596,46460124,1070653356,26650132164,
%T A321963 712373143716,20355134459004,619356569885676,20002325474150244,
%U A321963 683641504802995236,24662695086736585884,936845038595867508396,37388655553571504769924,1564425694139017014501156
%N A321963 Stieltjes generated from the sequence m, m+1, m+2, m+3, .... where m = 4.
%C A321963 See A321964 for the definitions.
%F A321963 a(n) ~ 2^(n + 5/2) * n^(n+3) / (3*exp(n)). - _Vaclav Kotesovec_, Jan 02 2019
%p A321963 A321963List := proc(len) local S, k, m, cf, ser;
%p A321963     S := [seq(k+4, k = 0..len)]: m := 1;
%p A321963     for k from len by -1 to 1 do
%p A321963         m := 1 - S[k]*x/m od;
%p A321963     cf := 1/m:
%p A321963     ser := series(cf, x, len);
%p A321963     seq(coeff(ser, x, n), n = 0..len-1) end:
%p A321963 A321963List(19);
%t A321963 T[n_, k_] := T[n, k] = If[k == n, n + 1, Sum[T[j + k, k] T[n - j, k + 1], {j, 0, n - k - 1}]]; a[n_] := T[n + 2, 2]/3; Table[a[n], {n, 0, 18}] (* _Jean-François Alcover_, Jul 22 2019, from A127059 *)
%Y A321963 A000007 (m=0), A001147 (m=1), A000698 (m=2), A167872 (m=3), this sequence (m=4).
%Y A321963 a(n) = A127059(n)/3.
%K A321963 nonn
%O A321963 0,2
%A A321963 _Peter Luschny_, Dec 26 2018