login
A126787
G.f.: B(x)*B(2!*x^2)*B(3!*x^3)*..., where B(x) is g.f. of A000142.
2
1, 1, 4, 14, 66, 308, 1888, 12240, 95640, 827904, 8106960, 87387264, 1035645312, 13316300928, 184988692800, 2756878875648, 43888205438208, 742943286892800, 13326434312808960, 252448071959572992, 5036116692383428608, 105523926692032447488
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
# 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 *)
CROSSREFS
Sequence in context: A305654 A241465 A320488 * A187742 A347432 A129219
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Feb 18 2007
EXTENSIONS
More terms from Alois P. Heinz, Sep 25 2008
STATUS
approved