%I A126787
%S A126787 1,1,4,14,66,308,1888,12240,95640,827904,8106960,87387264,1035645312,
%T A126787 13316300928,184988692800,2756878875648,43888205438208,742943286892800,
%U A126787 13326434312808960,252448071959572992,5036116692383428608
%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. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 
               Mar 21 2009]
%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); [From Alois 
               P. Heinz (heinz(AT)hs-heilbronn.de), Sep 25 2008]
%t A126787 CoefficientList[Series[Product[Sum[x^(n*k) n!^k*k!, {k, 0, 20}], {n, 
               1, 20}], {x, 0, 20}], x] [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 
               Mar 21 2009]
%Y A126787 Cf. A096161, A110143.
%Y A126787 Sequence in context: A020041 A081891 A119857 this_sequence A129219 A007025 
               A014512
%Y A126787 Adjacent sequences: A126784 A126785 A126786 this_sequence A126788 A126789 
               A126790
%K A126787 easy,nonn
%O A126787 0,3
%A A126787 Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 18 2007
%E A126787 More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 25 2008