|
|
A218261
|
|
E.g.f.: Sum_{n>=0} Product_{k=1..n} (exp((2*k-1)*x) - 1) / (2*k-1).
|
|
1
|
|
|
1, 1, 3, 19, 191, 2731, 52063, 1264747, 37912143, 1368247627, 58312623743, 2889264152875, 164299982895535, 10607439707069323, 770371122097072863, 62438253016068932203, 5608567981763102915087, 554952834214350689736139, 60161153106358242206145343
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
EXAMPLE
|
E.g.f.: A(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 191*x^4/4! + 2731*x^5/5! +...
where
A(x) = 1 + (exp(x)-1) + (exp(x)-1)*(exp(3*x)-1)/(1*3) + (exp(x)-1)*(exp(3*x)-1)*(exp(5*x)-1)/(1*3*5) + (exp(x)-1)*(exp(3*x)-1)*(exp(5*x)-1)*(exp(7*x)-1)/(1*3*5*7) +...
|
|
PROG
|
(PARI) {a(n)=local(X=x+x*O(x^n), Egf); Egf=sum(m=0, n, prod(k=1, m, (exp((2*k-1)*X)-1)/(2*k-1))); n!*polcoeff(Egf, n)}
for(n=0, 30, print1(a(n), ", "))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|