Voozh

A390374

Expansion of e.g.f. (1/3) * (exp(1/(1 - x)^3 - 1) + 2).

1, 1, 7, 65, 747, 10161, 158823, 2794401, 54510795, 1165346721, 27053090343, 676902963969, 18142447198923, 518153657647185, 15699151506800583, 502656646673908449, 16950329213158040427, 600210130556531336769, 22258602933289539520455, 862449563473679156954049, 34840561666808397518614827

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(n-k) * Stirling1(n,k) * Bell(k) * 3^(k-1) for n > 0.

a(n) = A202826(n) / 3 for n > 0.

MATHEMATICA

nmax = 20; CoefficientList[Series[(1/3) (Exp[1/(1 - x)^3 - 1] + 2), {x, 0, nmax}], x] Range[0, nmax]!

Join[{1}, Table[Sum[(-1)^(n - k) StirlingS1[n, k] BellB[k] 3^(k - 1), {k, 1, n}], {n, 1, 20}]]

CROSSREFS