A113671 Self-convolution 5th power equals A113665, where a(n) = n*A113665(n-1) for n>=1, with a(0)=1.

1, 1, 10, 180, 4440, 135525, 4866156, 199577910, 9174096960, 466435229220, 25973117225450, 1571873641094680, 102741164109622800, 7214517196021315830, 541781124945022815720, 43336510897320779553450

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

G.f. A(x) satisfies:

(1) A(x) = 1 + x*d/dx[x*A(x)^5],

(2) [x^n] exp( x*A(x)^5 ) * (n + 1 - A(x)) = 0 for n > 0,

(3) [x^n] exp( n * x*A(x)^5 ) * (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^5)); polcoeff(A, n, x)}

Crossrefs

Cf. A113665, A000699, A113669, A113670, A113672, A113673, A113674.

Sequence in context: A367986 A113119 A067416 * A001762 A034908 A030048

Adjacent sequences: A113668 A113669 A113670 * A113672 A113673 A113674

Keyword

nonn

Author

Paul D. Hanna, Nov 04 2005

Status

approved