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

%I A113674 #7 May 27 2018 20:41:31
%S A113674 1,1,16,468,18784,932030,54321840,3611129620,268687287744,
%T A113674 22085224470873,1986091468594160,193935237759263880,
%U A113674 20436302307290415264,2311999369405933686648,279558778132903394262032
%N A113674 Self-convolution 8th power equals A113668, where a(n) = n*A113668(n-1) for n>=1, with a(0)=1.
%F A113674 G.f. A(x) satisfies:
%F A113674 (1) A(x) = 1 + x*d/dx[x*A(x)^8],
%F A113674 (2) [x^n] exp( x*A(x)^8 ) * (n + 1 - A(x)) = 0 for n > 0,
%F A113674 (3) [x^n] exp( n * x*A(x)^8 ) * (2 - A(x)) = 0 for n > 0. - _Paul D. Hanna_, May 27 2018
%o A113674 (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)}
%Y A113674 Cf. A113668, A000699, A113669, A113670, A113671, A113672, A113673.
%K A113674 nonn
%O A113674 0,3
%A A113674 _Paul D. Hanna_, Nov 04 2005