A346922 Expansion of e.g.f. 1 / (1 + log(1 - x)^3 / 3!).

1, 0, 0, 1, 6, 35, 245, 2044, 19572, 210524, 2513760, 33012276, 472963876, 7340889192, 122703087416, 2197496734224, 41979155247520, 852063971170960, 18312093589455440, 415420659953439840, 9920128280950954080, 248735658391768241280, 6533773435848445617600

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..437

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * |Stirling1(k,3)| * a(n-k).

a(n) ~ n! * 6^(1/3) / (3 * exp(6^(1/3)) * (1 - exp(-6^(1/3)))^(n+1)). - Vaclav Kotesovec, Aug 08 2021

a(n) = Sum_{k=0..floor(n/3)} (3*k)! * |Stirling1(n,3*k)|/6^k. - Seiichi Manyama, May 06 2022

Mathematica

nmax = 22; CoefficientList[Series[1/(1 + Log[1 - x]^3/3!), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Abs[StirlingS1[k, 3]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 22}]

Prog

(PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1+log(1-x)^3/3!))) \\ Michel Marcus, Aug 07 2021
(PARI) a(n) = sum(k=0, n\3, (3*k)!*abs(stirling(n, 3*k, 1))/6^k); \\ Seiichi Manyama, May 06 2022

Crossrefs

Cf. A007840, A346921, A346923, A346924.

Cf. A000399, A346894, A347002, A353118.

Sequence in context: A346945 A289383 A249476 * A355381 A244267 A187443

Adjacent sequences: A346919 A346920 A346921 * A346923 A346924 A346925

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 07 2021

Status

approved