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

Author

Paul D. Hanna, Nov 05 2006

Keywords

• nonn

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.

Crossrefs

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

Programs

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]}

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.