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A371314
E.g.f. satisfies A(x) = -log(1 - x)/(1 - A(x))^2.
3
0, 1, 5, 56, 1022, 26054, 853426, 34150584, 1614418536, 88035438144, 5439554576064, 375580703703072, 28658577826251072, 2394815612176027104, 217504341217879448352, 21333409628052488832768, 2247318076016738768083200, 253054488675536428638723840
OFFSET
0,3
FORMULA
a(n) = Sum_{k=1..n} (3*k-2)!/(2*k-1)! * |Stirling1(n,k)|.
a(n) ~ n^(n-1) / (sqrt(2) * (exp(4/27) - 1)^(n - 1/2) * exp(23*n/27)). - Vaclav Kotesovec, Mar 19 2024
E.g.f.: Series_Reversion( 1 - exp(-x * (1 - x)^2) ). - Seiichi Manyama, Sep 08 2024
MAPLE
A371314 := proc(n)
add((3*k-2)!/(2*k-1)!*abs(stirling1(n, k)), k=1..n) ;
end proc:
seq(A371314(n), n=0..40) ; # R. J. Mathar, Mar 25 2024
MATHEMATICA
Table[Sum[(3*k-2)!/(2*k-1)! * Abs[StirlingS1[n, k]], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 19 2024 *)
PROG
(PARI) a(n) = sum(k=1, n, (3*k-2)!/(2*k-1)!*abs(stirling(n, k, 1)));
CROSSREFS
Cf. A370462.
Sequence in context: A217818 A217819 A132618 * A192562 A060080 A203522
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 18 2024
STATUS
approved