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Largest term in rows of triangle A126470, in which row sums equal factorials.
2

%I #4 Mar 30 2012 18:37:02

%S 1,1,1,3,7,26,136,784,5189,40639,357638,3472240,37835023,449901885,

%T 5763035223,79697811456,1185091117180,18789393725696,316557520950918,

%U 5664877511610114,106815500916218123,2123415404236087790

%N Largest term in rows of triangle A126470, in which row sums equal factorials.

%C 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 Row functions F(n,q) of triangle A126470 begin:

%e F(0,q) = F(1,q) = 1;

%e F(1,q) = 1 + q;

%e F(2,q) = 1 + 3*q + q^2 + q^3;

%e F(3,q) = 1 + 6*q + 7*q^2 + 5*q^3 + 3*q^4 + q^5 + q^6.

%o (PARI)

%Y Cf. A126470, A126471.

%K nonn

%O 0,4

%A _Paul D. Hanna_, Dec 31 2006