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

0,3

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.

Links

Table of n, a(n) for n=0..37.

Example

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.

Prog

(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]}

Crossrefs

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

Sequence in context: A237351 A299490 A361274 * A317100 A199932 A305552

Adjacent sequences: A126468 A126469 A126470 * A126472 A126473 A126474

Keyword

nonn

Author

Paul D. Hanna, Dec 31 2006

Status

approved