A168246 Inverse Weigh transform of n!.

1, 2, 4, 19, 92, 576, 4156, 34178, 314368, 3199936, 35703996, 433422071, 5687955724, 80256879068, 1211781887796, 19496946568898, 333041104402860, 6019770247224496, 114794574818830716, 2303332661419442569, 48509766592884311132, 1069983257387168051076

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..449

Formula

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

a(n) ~ n! * (1 - 1/n - 1/n^2 - 4/n^3 - 23/n^4 - 171/n^5 - 1542/n^6 - 16241/n^7 - 194973/n^8 - 2622610/n^9 - 39027573/n^10 - ...), for coefficients see A113869. - Vaclav Kotesovec, Nov 27 2020

Maple

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; n! -b(n, n-1) end:
seq(a(n), n=1..30);  # Alois P. Heinz, Jun 11 2018

Mathematica

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] = n! - b[n, n - 1];
Array[a, 30] (* Jean-François Alcover, Sep 16 2019, after Alois P. Heinz *)

Prog

(PARI) seq(n)={dirdiv(Vec(log(1+x*Ser(vector(n, n, n!)))), -vector(n, n, (-1)^n/n))} \\ Andrew Howroyd, Jun 22 2018

Crossrefs

Cf. A000142, A112354, A261052 (Weigh transform of n!).

Sequence in context: A289269 A363303 A272988 * A212923 A058130 A191563

Adjacent sequences: A168243 A168244 A168245 * A168247 A168248 A168249

Keyword

easy,nonn

Author

Vladeta Jovovic, Nov 21 2009

Status

approved