A193436 exp( Sum_{n>=1} x^n/n^3 ) = Sum_{n>=0} a(n)*x^n/n!^3.

1, 1, 5, 71, 2276, 144724, 16688884, 3249507820, 1005334796864, 468967172341824, 315409074574480704, 294510517409159769024, 369877735410388416241920, 608401340784471133062837504, 1281569707473914769353921666304, 3391681347749396029674738480747264

Offset

0,3

Comments

Sum_{n>=0} a(n)/n!^3 = exp(zeta(3)) = 3.326953110002499790...

Links

Table of n, a(n) for n=0..15.

Formula

a(0) = 1; a(n) = (n-1)! * (n!)^2 * Sum_{k=0..n-1} a(k) / ((k!)^3 * (n-k)^2). - Ilya Gutkovskiy, Jul 18 2020

Example

A(x) = 1 + x + 5*x^2/2!^3 + 71*x^3/3!^3 + 2276*x^4/4!^3 +...
where
log(A(x)) = x + x^2/8 + x^3/27 + x^4/64 + x^5/125 + x^6/216 +...

Prog

(PARI) {a(n)=n!^3*polcoeff(exp(sum(m=1, n, x^m/m^3)+x*O(x^n)), n)}

Crossrefs

Cf. A074707, A217145, A193435.

Sequence in context: A371326 A349471 A347989 * A193501 A133990 A326881

Adjacent sequences: A193433 A193434 A193435 * A193437 A193438 A193439

Keyword

nonn

Author

Paul D. Hanna, Jul 25 2011

Status

approved