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

1, 1, 3, 5, 12, 17, 39, 58, 108, 170, 310, 449, 791, 1181, 1960, 2915, 4668, 6822, 10842, 15818, 24254, 35061, 53213, 76061, 113822, 162631, 238660, 337764, 491319, 690530, 994390, 1391968, 1982724, 2757196, 3896450, 5382342, 7546547, 10384787

Offset: 0

Author

Paul D. Hanna, Dec 31 2006

Keywords

• nonn

Comments

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.

Examples

			Row functions F(n,q) of triangle A126470 begin:
F(0,q) = F(1,q) = 1;
F(1,q) = 1 + q;
F(2,q) = 1 + 3*q + q^2 + q^3;
F(3,q) = 1 + 6*q + 7*q^2 + 5*q^3 + 3*q^4 + q^5 + q^6.
		

Crossrefs

Cf. A126470, A126472; Bell number variant: A126348.

Programs

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]}