A113671 Self-convolution 5th power equals A113665, where a(n) = n*A113665(n-1) for n>=1, with a(0)=1.
1, 1, 10, 180, 4440, 135525, 4866156, 199577910, 9174096960, 466435229220, 25973117225450, 1571873641094680, 102741164109622800, 7214517196021315830, 541781124945022815720, 43336510897320779553450
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^5));polcoeff(A,n,x)}
Formula
G.f. A(x) satisfies:
(1) A(x) = 1 + x*d/dx[x*A(x)^5],
(2) [x^n] exp( x*A(x)^5 ) * (n + 1 - A(x)) = 0 for n > 0,
(3) [x^n] exp( n * x*A(x)^5 ) * (2 - A(x)) = 0 for n > 0. - Paul D. Hanna, May 27 2018