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A351274
a(0) = 1; thereafter a(n) = Sum_{k=1..n} (2*k)^k * Stirling1(n,k).
3
1, 2, 14, 172, 2964, 65848, 1789688, 57521280, 2133964352, 89744964288, 4219022123328, 219246630903936, 12479659844383104, 772174659456713472, 51603153976362554112, 3704166182571098222592, 284239227254465994240000, 23218955083323248158556160
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: 1/(1 + LambertW( -2 * log(1+x) )), where LambertW() is the Lambert W-function.
a(n) ~ n^n / (sqrt(2) * (exp(exp(-1)/2) - 1)^(n+1/2) * exp(n - exp(-1)/4 + 1/2)). - Vaclav Kotesovec, Feb 06 2022
MATHEMATICA
Join[{1}, Table[Sum[(2k)^k StirlingS1[n, k], {k, n}], {n, 20}]] (* Harvey P. Dale, Dec 31 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, (2*k)^k*stirling(n, k, 1));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(-2*log(1+x)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 05 2022
EXTENSIONS
Made a(0) = 1 explicit and changed range of k in definition to start at 1 at the suggestion of Harvey P. Dale. - N. J. A. Sloane, Dec 31 2023
STATUS
approved