login
A372316
Expansion of e.g.f. exp( x - LambertW(-3*x)/3 ).
4
1, 2, 10, 125, 2644, 77597, 2904382, 132169403, 7083715240, 437031850841, 30506442905194, 2377038378159359, 204521399708464252, 19259006462435865413, 1970114326513629358654, 217556451608123850352523, 25794252755430105917806288, 3268152272130255473300883377
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = Sum_{k=0..n} (3*k+1)^(k-1) * binomial(n,k).
G.f.: Sum_{k>=0} (3*k+1)^(k-1) * x^k / (1-x)^(k+1).
a(n) ~ 3^(n-1) * n^(n-1) * exp((exp(-1) + 1)/3). - Vaclav Kotesovec, May 04 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-3*x)/3)))
(PARI) a(n) = sum(k=0, n, (3*k+1)^(k-1)*binomial(n, k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 27 2024
STATUS
approved