A032268 "DIJ" (bracelet, indistinct, labeled) transform of 3,3,3,3,...

1, 3, 12, 57, 471, 6159, 105987, 2207847, 53715891, 1493742279, 46730999667, 1624397276487, 62111517207411, 2590839950614599, 117076879593900147, 5697526788322329927, 297074131510779228531, 16522357697381918530119, 976355872514689231565427

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

C. G. Bower, Transforms (2)

Formula

E.g.f.: 1 + (g(x) + g(x)^2/2 - log(1-g(x)))/2 where g(x) = 3*(exp(x) - 1). - Andrew Howroyd, Sep 12 2018

Mathematica

m = 19; (1 + (g[x] + g[x]^2/2 - Log[1 - g[x]])/2 /. g[x] -> 3*(Exp[x] - 1) + O[x]^m // CoefficientList[#, x]&)*Range[0, m-1]! (* Jean-François Alcover, Sep 11 2019 *)

Prog

(PARI) seq(n)={my(p=3*(exp(x + O(x*x^n))-1)); Vec(1 + serlaplace(p + p^2/2 - log(1-p))/2)} \\ Andrew Howroyd, Sep 12 2018

Crossrefs

Cf. A032266, A032267, A032269, A032270.

Sequence in context: A009248 A012709 A370528 * A079245 A122677 A038177

Adjacent sequences: A032265 A032266 A032267 * A032269 A032270 A032271

Keyword

nonn

Author

Christian G. Bower

Extensions

a(0)=1 prepended and terms a(17) and beyond from Andrew Howroyd, Sep 12 2018

Status

approved