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A217145 exp( Sum_{n>=1} x^n/n^4 ) = Sum_{n>=0} a(n)*x^n/n!^4. 4
1, 1, 9, 313, 30232, 6874776, 3355094696, 3302015131304, 6189229701416448, 20757720442141804032, 116803259505967824465408, 1039413737809909553149398528, 13914325979093456341597993070592, 268988472559744572003351007811825664 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Sum_{n>=0} a(n)/n!^4 = exp(Pi^4/90) = 2.951528682853355...
LINKS
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
Sequence in context: A231133 A163702 A160194 * A266835 A288324 A317634
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 18 2012
STATUS
approved

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Last modified July 13 18:54 EDT 2024. Contains 374285 sequences. (Running on oeis4.)