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A365584 Expansion of e.g.f. 1 / (1 + 4 * log(1-x))^(3/4). 1
1, 3, 24, 300, 5100, 109692, 2854344, 87164088, 3055516800, 120916282368, 5331444120576, 259168711406976, 13769882994784896, 793844510730348672, 49353915922852214016, 3291455140392403401984, 234388011123877880424960, 17750517946502792294592000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (4*j+3)) * |Stirling1(n,k)|.
a(0) = 1; a(n) = Sum_{k=1..n} (4 - k/n) * (k-1)! * binomial(n,k) * a(n-k).
a(n) ~ Gamma(1/4) * n^(n + 1/4) / (2^(3/2) * sqrt(Pi) * (exp(1/4) - 1)^(n + 3/4) * exp(3*n/4)). - Vaclav Kotesovec, Nov 11 2023
MATHEMATICA
a[n_] := Sum[Product[4*j + 3, {j, 0, k - 1}] * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Sep 10 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 4*j+3)*abs(stirling(n, k, 1)));
CROSSREFS
Cf. A365567.
Sequence in context: A292186 A365567 A258301 * A138209 A352235 A075142
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 10 2023
STATUS
approved

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Last modified April 23 03:30 EDT 2024. Contains 371906 sequences. (Running on oeis4.)