A306009 Inverse Weigh transform of A000085.

1, 2, 2, 7, 14, 43, 130, 446, 1544, 5773, 22170, 89356, 370198, 1591379, 7020014, 31922981, 148679262, 710828036, 3474337098, 17379964444, 88739068866, 462670294023, 2458638559154, 13317850411827, 73432568553848, 412120738922369, 2351720323257872

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..800

Formula

Product_{k>=1} (1+x^k)^a(k) = Sum_{n>=0} A000085(n) * x^n.

Maple

g:= proc(n) option remember;
      `if`(n<2, 1, g(n-1)+(n-1)*g(n-2))
    end:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= proc(n) option remember; g(n)-b(n, n-1) end:
seq(a(n), n=1..30);

Mathematica

g[n_] := g[n] = If[n < 2, 1, g[n - 1] + (n - 1)*g[n - 2]];
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[a[i], j]*b[n - i*j, i - 1], {j, 0, n/i}]]];
a[n_] := a[n] = g[n] - b[n, n - 1];
Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Oct 27 2021, after Alois P. Heinz *)

Crossrefs

Cf. A000085, A293114.

Sequence in context: A187306 A061274 A061575 * A290646 A133602 A137249

Adjacent sequences: A306006 A306007 A306008 * A306010 A306011 A306012

Keyword

nonn

Author

Alois P. Heinz, Jun 16 2018

Status

approved