A217145 exp( Sum_{n>=1} x^n/n^4 ) = Sum_{n>=0} a(n)*x^n/n!^4.

1, 1, 9, 313, 30232, 6874776, 3355094696, 3302015131304, 6189229701416448, 20757720442141804032, 116803259505967824465408, 1039413737809909553149398528, 13914325979093456341597993070592, 268988472559744572003351007811825664

Offset

0,3

Comments

Sum_{n>=0} a(n)/n!^4 = exp(Pi^4/90) = 2.951528682853355...

Links

Table of n, a(n) for n=0..13.

Formula

a(0) = 1; a(n) = (n-1)! * (n!)^3 * Sum_{k=0..n-1} a(k) / ((k!)^4 * (n-k)^3). - Ilya Gutkovskiy, Jul 18 2020

Example

A(x) = 1 + x + 9*x^2/2!^4 + 313*x^3/3!^4 + 30232*x^4/4!^4 + 6874776*x^5/5!^4 +...
where
log(A(x)) = x + x^2/2^4 + x^3/3^4 + x^4/4^4 + x^5/5^3 + x^6/6^4 +...

Prog

(PARI) {a(n)=n!^4*polcoeff(exp(sum(m=1, n, x^m/m^4)+x*O(x^n)), n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A074707, A193436.

Sequence in context: A231133 A163702 A160194 * A266835 A288324 A317634

Adjacent sequences: A217142 A217143 A217144 * A217146 A217147 A217148

Keyword

nonn

Author

Paul D. Hanna, Oct 18 2012

Status

approved