A051529 INVERT transform of A000081 = [1, 1, 1, 2, 4, 9, 20, 48, 115, 286,...].

1, 2, 4, 9, 21, 51, 126, 318, 812, 2100, 5482, 14438, 38303, 102302, 274824, 742210, 2013941, 5488239, 15014376, 41221775, 113542455, 313681756, 868994723, 2413526848, 6719132105, 18746838609, 52412080624, 146812972155, 411977724704, 1158006098132

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..650

Crossrefs

Cf. A000081, A000107.

Programs

Maple

with(numtheory): b:= proc(n) option remember; local d, j; `if`(n<=1, 1, (add(add(d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/ (n-1)) end: a:= proc(n) option remember; local i; `if`(n<1, 1, add(a(n-i) *b(i-1), i=1..n+1)) end: seq(a(n), n=0..30);  # Alois P. Heinz, Apr 01 2009

Mathematica

b[n_] := b[n] = If[n <= 1, 1, (Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n - j], {j, 1, n - 1}])/ (n - 1)];
a[n_] := a[n] = If[n < 1, 1, Sum[a[n - i]*b[i - 1], {i, 1, n + 1}]];
a /@ Range[0, 30] (* Jean-François Alcover, Mar 01 2021, after Alois P. Heinz *)