A113674 Self-convolution 8th power equals A113668, where a(n) = n*A113668(n-1) for n>=1, with a(0)=1.

1, 1, 16, 468, 18784, 932030, 54321840, 3611129620, 268687287744, 22085224470873, 1986091468594160, 193935237759263880, 20436302307290415264, 2311999369405933686648, 279558778132903394262032

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

G.f. A(x) satisfies:

(1) A(x) = 1 + x*d/dx[x*A(x)^8],

(2) [x^n] exp( x*A(x)^8 ) * (n + 1 - A(x)) = 0 for n > 0,

(3) [x^n] exp( n * x*A(x)^8 ) * (2 - A(x)) = 0 for n > 0. - Paul D. Hanna, May 27 2018

Prog

(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=1, n, A=1+x*deriv(x*A^8)); polcoeff(A, n, x)}

Crossrefs

Cf. A113668, A000699, A113669, A113670, A113671, A113672, A113673.

Sequence in context: A368772 A253446 A159646 * A281834 A299078 A299841

Adjacent sequences: A113671 A113672 A113673 * A113675 A113676 A113677

Keyword

nonn

Author

Paul D. Hanna, Nov 04 2005

Status

approved