cp's OEIS Frontend

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

%I A113672 #9 May 27 2018 20:39:49
%S A113672 1,1,12,261,7784,287145,12452256,616408534,34178166288,2094929612766,
%T A113672 140568321437700,10246761825942972,806426083421461440,
%U A113672 68162575162983744079,6159817390723312545936,592796927295190983761100
%N A113672 Self-convolution 6th power equals A113666, where a(n) = n*A113666(n-1) for n>=1, with a(0)=1.
%F A113672 G.f. A(x) satisfies:
%F A113672 (1) A(x) = 1 + x*d/dx[x*A(x)^6],
%F A113672 (2) [x^n] exp( x*A(x)^6 ) * (n + 1 - A(x)) = 0 for n > 0,
%F A113672 (3) [x^n] exp( n * x*A(x)^6 ) * (2 - A(x)) = 0 for n > 0. - _Paul D. Hanna_, May 27 2018
%o A113672 (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)}
%Y A113672 Cf. A113666, A000699, A113669, A113670, A113671, A113673, A113674.
%K A113672 nonn
%O A113672 0,3
%A A113672 _Paul D. Hanna_, Nov 04 2005