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 A217145 exp( Sum_{n>=1} x^n/n^4 )  =  Sum_{n>=0} a(n)*x^n/n!^4. 2

%I

%S 1,1,9,313,30232,6874776,3355094696,3302015131304,6189229701416448,

%T 20757720442141804032,116803259505967824465408,

%U 1039413737809909553149398528,13914325979093456341597993070592,268988472559744572003351007811825664

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

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

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

%e where

%e log(A(x)) = x + x^2/2^4 + x^3/3^4 + x^4/4^4 + x^5/5^3 + x^6/6^4 +...

%o (PARI) {a(n)=n!^4*polcoeff(exp(sum(m=1, n, x^m/m^4)+x*O(x^n)), n)}

%o for(n=0,20,print1(a(n),", "))

%Y Cf. A074707, A193436.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 18 2012

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Last modified December 12 12:30 EST 2019. Contains 329958 sequences. (Running on oeis4.)