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A126471 Limit of reversed rows of triangle A126470, in which row sums equal the factorials. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A203150 A237351 A299490 * A317100 A199932 A305552

Adjacent sequences:  A126468 A126469 A126470 * A126472 A126473 A126474

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 31 2006

STATUS

approved

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Last modified May 9 13:35 EDT 2021. Contains 343742 sequences. (Running on oeis4.)