cp's OEIS Frontend

A113670 Self-convolution 4th power equals A113664, where a(n) = n*A113664(n-1) for n>=1, with a(0)=1.

%I A113670 #12 May 27 2018 20:38:40
%S A113670 1,1,8,114,2224,53725,1528200,49703108,1813503712,73247619060,
%T A113670 3242579748000,156107189374202,8121266448765936,454110696002834806,
%U A113670 27165980379205109232,1731608155057922555400,117183510733473232477120
%N A113670 Self-convolution 4th power equals A113664, where a(n) = n*A113664(n-1) for n>=1, with a(0)=1.
%F A113670 G.f. A(x) satisfies:
%F A113670 (1) A(x) = 1 + x*d/dx[x*A(x)^4],
%F A113670 (2) [x^n] exp( x*A(x)^4 ) * (n + 1 - A(x)) = 0 for n > 0,
%F A113670 (3) [x^n] exp( n * x*A(x)^4 ) * (2 - A(x)) = 0 for n > 0. - _Paul D. Hanna_, May 27 2018
%o A113670 (PARI) {a(n)=local(A=1+x*O(x^n));for(i=1,n, A=1+x*deriv(x*A^4));polcoeff(A,n,x)}
%Y A113670 Cf. A113664, A000699, A113669, A113671, A113672, A113673, A113674.
%K A113670 nonn
%O A113670 0,3
%A A113670 _Paul D. Hanna_, Nov 04 2005