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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

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)

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

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

# Alternative:

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 *)

CROSSREFS

Cf. A096161, A110143.

Sequence in context: A382861 A241465 A320488 * A187742 A347432 A129219

Adjacent sequences: A126784 A126785 A126786 * A126788 A126789 A126790