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

1, 4, 36, 444, 6636, 114084, 2194596, 46460124, 1070653356, 26650132164, 712373143716, 20355134459004, 619356569885676, 20002325474150244, 683641504802995236, 24662695086736585884, 936845038595867508396, 37388655553571504769924, 1564425694139017014501156

Offset: 0

Author

Peter Luschny, Dec 26 2018

Keywords

• nonn

Comments

See A321964 for the definitions.

Crossrefs

A000007 (m=0), A001147 (m=1), A000698 (m=2), A167872 (m=3), this sequence (m=4).

a(n) = A127059(n)/3.

Programs

Maple

A321963List := proc(len) local S, k, m, cf, ser;
    S := [seq(k+4, k = 0..len)]: m := 1;
    for k from len by -1 to 1 do
        m := 1 - S[k]*x/m od;
    cf := 1/m:
    ser := series(cf, x, len);
    seq(coeff(ser, x, n), n = 0..len-1) end:
A321963List(19);

Mathematica

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 *)

Formula

a(n) ~ 2^(n + 5/2) * n^(n+3) / (3*exp(n)). - Vaclav Kotesovec, Jan 02 2019