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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.

%I A126787 #26 Oct 02 2017 15:17:55
%S A126787 1,1,4,14,66,308,1888,12240,95640,827904,8106960,87387264,1035645312,
%T A126787 13316300928,184988692800,2756878875648,43888205438208,
%U A126787 742943286892800,13326434312808960,252448071959572992,5036116692383428608,105523926692032447488
%N A126787 G.f.: B(x)*B(2!*x^2)*B(3!*x^3)*..., where B(x) is g.f. of A000142.
%C A126787 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
%H A126787 Alois P. Heinz, <a href="/A126787/b126787.txt">Table of n, a(n) for n = 0..450</a> (terms n=176..300 from Vaclav Kotesovec)
%F A126787 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
%p A126787 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
%p A126787 # second Maple program:
%p A126787 b:= proc(n, i) option remember; `if`(n=0 or i=1, n!,
%p A126787       add(b(n-i*j, i-1)*j!*i!^j, j=0..n/i))
%p A126787     end:
%p A126787 a:= n-> b(n$2):
%p A126787 seq(a(n), n=0..30);  # _Alois P. Heinz_, Oct 02 2017
%t A126787 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 *)
%Y A126787 Cf. A096161, A110143.
%K A126787 easy,nonn
%O A126787 0,3
%A A126787 _Vladeta Jovovic_, Feb 18 2007
%E A126787 More terms from _Alois P. Heinz_, Sep 25 2008