A113672 Self-convolution 6th power equals A113666, where a(n) = n*A113666(n-1) for n>=1, with a(0)=1.

1, 1, 12, 261, 7784, 287145, 12452256, 616408534, 34178166288, 2094929612766, 140568321437700, 10246761825942972, 806426083421461440, 68162575162983744079, 6159817390723312545936, 592796927295190983761100

Offset: 0

Author

Paul D. Hanna, Nov 04 2005

Keywords

• nonn

Crossrefs

Cf. A113666, A000699, A113669, A113670, A113671, A113673, A113674.

Programs

PARI

{a(n)=local(A=1+x*O(x^n));for(i=1,n, A=1+x*deriv(x*A^6));polcoeff(A,n,x)}

Formula

G.f. A(x) satisfies:

(1) A(x) = 1 + x*d/dx[x*A(x)^6],

(2) [x^n] exp( x*A(x)^6 ) * (n + 1 - A(x)) = 0 for n > 0,

(3) [x^n] exp( n * x*A(x)^6 ) * (2 - A(x)) = 0 for n > 0. - Paul D. Hanna, May 27 2018