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A193436 exp( Sum_{n>=1} x^n/n^3 )  =  Sum_{n>=0} a(n)*x^n/n!^3. 5
1, 1, 5, 71, 2276, 144724, 16688884, 3249507820, 1005334796864, 468967172341824, 315409074574480704, 294510517409159769024, 369877735410388416241920, 608401340784471133062837504, 1281569707473914769353921666304, 3391681347749396029674738480747264 (list; graph; refs; listen; history; text; internal format)
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: A064752 A033507 A092250 * A193501 A133990 A326881

Adjacent sequences:  A193433 A193434 A193435 * A193437 A193438 A193439

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 25 2011

STATUS

approved

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Last modified March 8 23:14 EST 2021. Contains 341959 sequences. (Running on oeis4.)