A113674 Self-convolution 8th power equals A113668, where a(n) = n*A113668(n-1) for n>=1, with a(0)=1.
1, 1, 16, 468, 18784, 932030, 54321840, 3611129620, 268687287744, 22085224470873, 1986091468594160, 193935237759263880, 20436302307290415264, 2311999369405933686648, 279558778132903394262032
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^8));polcoeff(A,n,x)}
Formula
G.f. A(x) satisfies:
(1) A(x) = 1 + x*d/dx[x*A(x)^8],
(2) [x^n] exp( x*A(x)^8 ) * (n + 1 - A(x)) = 0 for n > 0,
(3) [x^n] exp( n * x*A(x)^8 ) * (2 - A(x)) = 0 for n > 0. - Paul D. Hanna, May 27 2018