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

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..350

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

Prog

(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)}

Crossrefs

Cf. A113663, A000699, A113670, A113671, A113672, A113673, A113674.

Sequence in context: A302103 A229451 A132078 * A340912 A121415 A227278

Adjacent sequences: A113666 A113667 A113668 * A113670 A113671 A113672

Keyword

nonn

Author

Paul D. Hanna, Nov 04 2005

Status

approved