OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..160
FORMULA
a(n) ~ c * d^n * (n!)^3 / n^2, where d = r^3*(1+exp(2/r)) = 7.8512435106631367719817991716164612615296980032514..., r = 0.94520217245242431308104743874492469552738... is the root of the equation (1+exp(-2/r))*LambertW(-exp(-1/r)/r) = -1/r, and c = 0.15095210978787998524366903417512193343948127919...
E.g.f.: Sum_{k>=1} (exp(k^2*x) - 1)^k / k. - Seiichi Manyama, Jun 19 2024
MATHEMATICA
Table[Sum[k^(2*n-1) * k! * StirlingS2[n, k], {k, 1, n}], {n, 1, 20}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, May 08 2014
STATUS
approved