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A126471 Limit of reversed rows of triangle A126470, in which row sums equal the factorials.

%I A126471 #4 Mar 30 2012 18:37:02
%S A126471 1,1,3,5,12,17,39,58,108,170,310,449,791,1181,1960,2915,4668,6822,
%T A126471 10842,15818,24254,35061,53213,76061,113822,162631,238660,337764,
%U A126471 491319,690530,994390,1391968,1982724,2757196,3896450,5382342,7546547,10384787
%N A126471 Limit of reversed rows of triangle A126470, in which row sums equal the factorials.
%C A126471 In triangle A126470, row n lists coefficients of q in F(n,q) that satisfies: F(n,q) = Sum_{k=0..n-1} C(n-1,k)*F(k,q)*F(n-k-1,q)*q^k for n>0, with F(0,q) = 1.
%e A126471 Row functions F(n,q) of triangle A126470 begin:
%e A126471 F(0,q) = F(1,q) = 1;
%e A126471 F(1,q) = 1 + q;
%e A126471 F(2,q) = 1 + 3*q + q^2 + q^3;
%e A126471 F(3,q) = 1 + 6*q + 7*q^2 + 5*q^3 + 3*q^4 + q^5 + q^6.
%o A126471 (PARI) {F(n,q)=if(n==0,1,sum(k=0,n-1,binomial(n-1,k)*F(k,q)*F(n-k-1,q)*q^k))} {a(n)=Vec(F(n+1,q)+O(q^(n*(n-1)/2+1)))[n*(n-1)/2+1]}
%Y A126471 Cf. A126470, A126472; Bell number variant: A126348.
%K A126471 nonn
%O A126471 0,3
%A A126471 _Paul D. Hanna_, Dec 31 2006