A193436 - OEIS

The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

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 (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 + 5x^2/2!^3 + 71x^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!^3polcoeff(exp(sum(m=1, n, x^m/m^3)+xO(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`

License Agreements, Terms of Use, Privacy Policy. .

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