|
|
A248657
|
|
E.g.f.: Sum_{n>=0} exp(n^2*(n+1)/2*x) / (1 + exp(n^2*x))^(n+1) = Sum_{n>=0} a(n) * x^(2*n) / (2*n)!.
|
|
1
|
|
|
1, -154, 22885622, -67465813019194, 1437168237462688869782, -134874257420380161852790174234, 41492847795963159872255018412799196342, -34364863511758593932657779153553482763524487674, 66563566600887661498498837311669792149014849464660729302
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Compare to an e.g.f. of A248656: Sum_{n>=0} exp(n*(n+1)/2*x)/(1 + exp(n*x))^(n+1).
|
|
LINKS
|
|
|
EXAMPLE
|
E.g.f.: A(x) = 1 - 154*x^2/2! + 22885622*x^4/4! - 67465813019194*x^6/6! +-...
where
A(x) = 1/2 + exp(x)/(1+exp(x))^2 + exp(6*x)/(1+exp(4*x))^3 + exp(18*x)/(1+exp(9*x))^4 + exp(40*x)/(1+exp(16*x))^5 + exp(75*x)/(1+exp(25*x))^6 +...
|
|
PROG
|
(PARI) \p200 \\ set precision
{A=Vec(serlaplace(sum(n=0, 800, 1.*exp(n^2*(n+1)/2*x +O(x^31))/(1 + exp(n^2*x +O(x^31)))^(n+1)) ))}
for(n=1, #A\2, print1(round(A[2*n-1]), ", "))
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|