A124545 Row 5 of rectangular table A124540; equals the self-convolution 5th power of A124535 (row 5 of table A124530).

1, 5, 40, 285, 1995, 13976, 98665, 704810, 5107950, 37619020, 281850156, 2149737335, 16700012890, 132177206400, 1066116496055, 8764513792396, 73445461419380, 627378087294215, 5462723243482985, 48480560040789335

Offset

0,2

Comments

In table A124540, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = [ Sum_{k>=0} y^k*R_k(y)^n ]^n for n>=0.

Links

Table of n, a(n) for n=0..19.

Formula

G.f.: A(x) = [ Sum_{n>=0} x^n*R_n(x)^5 ]^5, where R_n(x) is the g.f. of row n in table A124540.

Prog

(PARI) {a(n)=local(R); R=vector(n+6, r, vector(n+6, c, 1)); for(i=0, n+5, for(r=0, n+5, R[r+1]=Vec(sum(c=0, n, x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); Vec(Ser(R[6])^5+O(x^(n+1)))[n+1]}

Crossrefs

Cf. A124535; A124540 (table); other rows: A124531, A124542, A124543, A124544, A124546.

Sequence in context: A087632 A229279 A124306 * A125729 A144069 A280158

Adjacent sequences: A124542 A124543 A124544 * A124546 A124547 A124548

Keyword

nonn

Author

Paul D. Hanna, Nov 05 2006

Status

approved