A052251 Column 3 of A052250.

1, 3, 6, 13, 27, 63, 148, 363, 912, 2330, 6036, 15825, 41865, 111636, 299736, 809513, 2197728, 5994219, 16416748, 45129396, 124479270, 344403494, 955557780, 2658061560, 7411457963, 20710700277, 57992124810, 162691293718, 457219737027, 1287065977413

Offset: 3

Author

David Broadhurst, Feb 05 2000

Keywords

• nonn

Comments

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..700

Crossrefs

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

Cf. A051491.

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)^3, x, n-3): seq(a(n), n=3..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, 3];
a /@ Range[3, 35] (* Jean-François Alcover, Nov 09 2020, after Alois P. Heinz *)

Formula

a(n) ~ c * d^n / n^(3/2), where d = A051491 = 2.9557652856519949747148175241..., c = 0.195489104191039910520879642... . - Vaclav Kotesovec, Sep 05 2014

Extensions

More terms from Alois P. Heinz, Oct 23 2009