A113673 Self-convolution 7th power equals A113667, where a(n) = n*A113667(n-1) for n>=1, with a(0)=1.
1, 1, 14, 357, 12488, 540155, 27453258, 1591997162, 103362754048, 7415833578300, 582246803894350, 49648781879763836, 4569614321483063496, 451606519694514555917, 47709061981854231868308
Offset: 0
Keywords
Programs
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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)}
Formula
G.f. A(x) satisfies:
(1) A(x) = 1 + x*d/dx[x*A(x)^7],
(2) [x^n] exp( x*A(x)^7 ) * (n + 1 - A(x)) = 0 for n > 0,
(3) [x^n] exp( n * x*A(x)^7 ) * (2 - A(x)) = 0 for n > 0. - Paul D. Hanna, May 27 2018