A126787 G.f.: B(x)*B(2!*x^2)*B(3!*x^3)*..., where B(x) is g.f. of A000142.

1, 1, 4, 14, 66, 308, 1888, 12240, 95640, 827904, 8106960, 87387264, 1035645312, 13316300928, 184988692800, 2756878875648, 43888205438208, 742943286892800, 13326434312808960, 252448071959572992, 5036116692383428608, 105523926692032447488

Offset: 0

Author

Vladeta Jovovic, Feb 18 2007

Keywords

• easy
• nonn

Comments

Take each Ferrers diagram of the partitions of n, label(linearly order) the dots within each row, then linearly order any of the rows that are of equal length. - Geoffrey Critzer, Mar 21 2009

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450 (terms n=176..300 from Vaclav Kotesovec)

Crossrefs

Cf. A096161, A110143.

Programs

Maple

B:= proc(n) option remember; local x; unapply(`if`(n<=0, 1, B(n-1)(x)+ n! *x^n), x) end: BB:= proc(n) local x, d; unapply(convert(series(mul(B(floor(n/d))(d!*x^d), d=1..n), x, n+1), polynom), x) end: a:= n-> coeff(BB(n)(x), x, n): seq(a(n), n=0..25); # Alois P. Heinz, Sep 25 2008
# second Maple program:
b:= proc(n, i) option remember; `if`(n=0 or i=1, n!,
      add(b(n-i*j, i-1)*j!*i!^j, j=0..n/i))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..30);  # Alois P. Heinz, Oct 02 2017

Mathematica

CoefficientList[Series[Product[Sum[x^(n*k) n!^k*k!, {k, 0, 20}], {n, 1, 20}], {x, 0, 20}], x] (* Geoffrey Critzer, Mar 21 2009 *)

Formula

a(n) ~ 2*n! * (1 + 1/(2*n) + 3/n^2 + 13/n^3 + 82/n^4 + 587/n^5 + 4966/n^6). - Vaclav Kotesovec, Mar 16 2015

Extensions

More terms from Alois P. Heinz, Sep 25 2008