cp's OEIS Frontend

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

%I A113671 #13 Jun 07 2018 22:26:02
%S A113671 1,1,10,180,4440,135525,4866156,199577910,9174096960,466435229220,
%T A113671 25973117225450,1571873641094680,102741164109622800,
%U A113671 7214517196021315830,541781124945022815720,43336510897320779553450
%N A113671 Self-convolution 5th power equals A113665, where a(n) = n*A113665(n-1) for n>=1, with a(0)=1.
%F A113671 G.f. A(x) satisfies:
%F A113671 (1) A(x) = 1 + x*d/dx[x*A(x)^5],
%F A113671 (2) [x^n] exp( x*A(x)^5 ) * (n + 1 - A(x)) = 0 for n > 0,
%F A113671 (3) [x^n] exp( n * x*A(x)^5 ) * (2 - A(x)) = 0 for n > 0. - _Paul D. Hanna_, May 27 2018
%o A113671 (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)}
%Y A113671 Cf. A113665, A000699, A113669, A113670, A113672, A113673, A113674.
%K A113671 nonn
%O A113671 0,3
%A A113671 _Paul D. Hanna_, Nov 04 2005