A113669 Self-convolution cube equals A113663, where a(n) = n*A113663(n-1) for n>=1, with a(0)=1.
1, 1, 6, 63, 904, 16080, 337374, 8107743, 218940480, 6554205342, 215319184860, 7701064928370, 297912862462680, 12396725926132990, 552257670588677214, 26229243983909050215, 1323230977463353055616, 70673562984581535191094
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..350
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^3));polcoeff(A,n,x)}
Formula
G.f. A(x) satisfies:
(1) A(x) = 1 + x*d/dx[x*A(x)^3],
(2) [x^n] exp( x*A(x)^3 ) * (n + 1 - A(x)) = 0 for n > 0,
(3) [x^n] exp( n * x*A(x)^3 ) * (2 - A(x)) = 0 for n > 0. - Paul D. Hanna, May 27 2018
From Vaclav Kotesovec, Oct 23 2020: (Start)
a(n) ~ c * 3^n * n! * n^(2/3), where c = 0.2509528330393045762351289...
a(n) ~ A113663(n)/3. (End)
a(0) = 1; a(n) = n * Sum_{i=0..n-1} Sum_{j=0..n-i-1} a(i) * a(j) * a(n-i-j-1). - Ilya Gutkovskiy, Jul 25 2021