|
|
A367134
|
|
E.g.f. satisfies A(x) = 1/(2 - exp(x*A(x)^2)).
|
|
4
|
|
|
1, 1, 7, 97, 2051, 58681, 2122695, 92960001, 4782826459, 282821367001, 18901822316543, 1409070858589153, 115925274671836371, 10433564954705754681, 1019782291631652745591, 107570331041074850633473, 12180277895590328004331019, 1473587743517654702900335705
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (1/(2*n+1)!) * Sum_{k=0..n} (2*n+k)! * Stirling2(n,k).
a(n) ~ 2^(n-1) * LambertW(exp(1/2))^(2*n + 1) * n^(n-1) / (sqrt(1 + LambertW(exp(1/2))) * exp(n) * (2*LambertW(exp(1/2)) - 1)^(3*n + 1)). - Vaclav Kotesovec, Nov 07 2023
|
|
MATHEMATICA
|
Table[1/(2*n+1)! * Sum[(2*n+k)! * StirlingS2[n, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 07 2023 *)
|
|
PROG
|
(PARI) a(n) = sum(k=0, n, (2*n+k)!*stirling(n, k, 2))/(2*n+1)!;
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|