A052252 Column 4 of A052250.

1, 4, 10, 24, 55, 132, 322, 804, 2051, 5304, 13886, 36716, 97882, 262756, 709658, 1926748, 5255707, 14396048, 39580338, 109190052, 302148814, 838449236, 2332652648, 6505071080, 18180441512, 50914047384, 142853059922, 401517522844, 1130400537667, 3187335556064

Offset: 4

Author

David Broadhurst, Feb 05 2000

Keywords

• nonn

Comments

Also expansion of 4th power of g.f. for A051573. - Alois P. Heinz, Oct 23 2009

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..500

Crossrefs

Cf. A051573, A000081. - Alois P. Heinz, Oct 23 2009

Programs

Maple

with(numtheory): A81:= proc(n) option remember; `if`(n<2, n, (add(add(d*A81(d), d=divisors(j)) *A81(n-j), j=1..n-1))/ (n-1)) end: b:= proc(n) option remember; -`if`(n<0, 1, add(b(n-i) *A81(i+1), i=1..n+1)) end: B:= proc(n) add(b(i) *x^i, i=0..n) end: a:= n-> coeff(B(n)^4, x, n-4): seq(a(n), n=4..35); # Alois P. Heinz, Oct 23 2009

Mathematica

A81[n_] := A81[n] = If[n < 2, n, Sum[Sum[d A81[d], {d, Divisors[j]}] A81[n - j], {j, 1, n - 1}]/(n - 1)];
b[n_] := b[n] = -If[n < 0, 1, Sum[b[n - i] A81[i + 1], {i, 1, n + 1}]];
B[n_] := Sum[b[i] x^i, {i, 0, n}];
T[n_, k_] := Coefficient[B[n]^k, x, n - k];
a[n_] := T[n, 4];
a /@ Range[4, 35] (* Jean-François Alcover, Nov 09 2020, after Alois P. Heinz *)

Formula

a(n) ~ c * d^n / n^(3/2), where d = A051491 = 2.9557652856519949747148..., c = 0.17246782327675280347707... . - Vaclav Kotesovec, Sep 06 2014

Extensions

More terms from Alois P. Heinz, Oct 23 2009