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A371318
E.g.f. satisfies A(x) = exp(x) + x*A(x)^3.
2
1, 2, 13, 190, 4345, 135346, 5345749, 256004974, 14416470961, 933597699202, 68358972056221, 5584583237569150, 503607231488672425, 49690178089937051122, 5325031693664693833957, 615922452708451717999726, 76479190243720703567763553
OFFSET
0,2
FORMULA
a(n) = n! * Sum_{k=0..n} (2*k+1)^(n-k-1) * binomial(3*k,k)/(n-k)!.
a(n) ~ sqrt(1 + LambertW(8/27)) * 2^n * n^(n-1) / (3 * exp(n) * LambertW(8/27)^(n + 1/2)). - Vaclav Kotesovec, Jun 01 2024
MATHEMATICA
Table[n! Sum[(2 k + 1)^(n - k - 1)*Binomial[3 k, k]/(n - k)!, {k, 0, n}], {n, 0, 20}] (* Wesley Ivan Hurt, May 25 2024 *)
PROG
(PARI) a(n) = n!*sum(k=0, n, (2*k+1)^(n-k-1)*binomial(3*k, k)/(n-k)!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 18 2024
STATUS
approved