%I #7 May 27 2018 20:40:36

%S 1,1,14,357,12488,540155,27453258,1591997162,103362754048,

%T 7415833578300,582246803894350,49648781879763836,4569614321483063496,

%U 451606519694514555917,47709061981854231868308

%N Self-convolution 7th power equals A113667, where a(n) = n*A113667(n-1) for n>=1, with a(0)=1.

%F G.f. A(x) satisfies:

%F (1) A(x) = 1 + x*d/dx[x*A(x)^7],

%F (2) [x^n] exp( x*A(x)^7 ) * (n + 1 - A(x)) = 0 for n > 0,

%F (3) [x^n] exp( n * x*A(x)^7 ) * (2 - A(x)) = 0 for n > 0. - _Paul D. Hanna_, May 27 2018

%o (PARI) {a(n)=local(A=1+x*O(x^n));for(i=1,n, A=1+x*deriv(x*A^7));polcoeff(A,n,x)}

%Y Cf. A113667, A000699, A113669, A113670, A113671, A113672, A113674.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 04 2005