|
|
A370877
|
|
Expansion of e.g.f. (1/x) * Series_Reversion( x/(x + exp(x^2/2)) ).
|
|
1
|
|
|
1, 1, 3, 15, 111, 1095, 13605, 204225, 3597825, 72788625, 1663323795, 42373980495, 1190822561775, 36596898673335, 1221033470181525, 43954996792932225, 1698138394110583425, 70082689941923083425, 3077205709746516423075, 143235112906380591471375
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = n! * Sum_{k=0..floor(n/2)} (2*k+1)^(k-1) * binomial(n,2*k)/(2^k * k!).
|
|
PROG
|
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(x+exp(x^2/2)))/x))
(PARI) a(n) = n!*sum(k=0, n\2, (2*k+1)^(k-1)*binomial(n, 2*k)/(2^k*k!));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|