A352113 Expansion of e.g.f. (1 - log(1 - 3*x))^(1/3).

1, 1, 1, 10, 64, 874, 11602, 214696, 4287376, 102791944, 2706467608, 80520419440, 2616373545040, 93309672227680, 3598524149027680, 149819807423180800, 6681701058862660480, 318224146460638476160, 16106859257541255648640, 863764371283534316220160

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..n} (-3)^(n-k) * (Product_{j=0..k-1} (-3*j+1)) * Stirling1(n,k).

a(n) ~ n! * 3^(n-1) / (log(n)^(2/3) * n) * (1 - 2*(gamma + 1)/(3*log(n))), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Mar 05 2022

Mathematica

m = 19; Range[0, m]! * CoefficientList[Series[(1 - Log[1 - 3*x])^(1/3), {x, 0, m}], x] (* Amiram Eldar, Mar 05 2022 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((1-log(1-3*x))^(1/3)))
(PARI) a(n) = sum(k=0, n, (-3)^(n-k)*prod(j=0, k-1, -3*j+1)*stirling(n, k, 1));

Crossrefs

Cf. A352075, A352114.

Cf. A352070.

Sequence in context: A249978 A199487 A144041 * A286070 A033908 A033863

Adjacent sequences: A352110 A352111 A352112 * A352114 A352115 A352116

Keyword

nonn

Author

Seiichi Manyama, Mar 05 2022

Status

approved