A133148 E.g.f.: Sum_{k>=1} (x^k/k! / Product_{i=1..k} (1-x^i)).

1, 3, 10, 53, 286, 2227, 16682, 164089, 1619506, 19139231, 228289282, 3233324437, 45177961154, 727739459371, 11876754782146, 215081192780657, 3943187021584642, 80187760712122039, 1635670770628012706

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..400

Formula

E.g.f.: let B(x)=(1 - G(0))/(1-x) where G(k) = 1 - 1/(1-x^(k+1))/(k+1)/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction); then the e.g.f. equals d/dx B(x). - Sergei N. Gladkovskii, Jan 22 2013

Maple

A133148 := proc(n) local egf, k, i, tmp; egf := 0 ; for k from 1 to n do tmp := x^k/k! ; for i from 1 to k do tmp := taylor( tmp/(1-x^i), x=0, n+1) ; od: egf := egf+tmp ; od: coeftayl(egf*n!, x=0, n) ; end: seq(A133148(n), n=1..25) ; # R. J. Mathar, Sep 28 2007

Mathematica

Rest[ Range[0, 15]!* CoefficientList[ Series[ Sum[x^k/k!/Product[(1 - x^i), {i, k}], {k, 15}], {x, 0, 15}], x]] (* Robert G. Wilson v, Oct 07 2007 *)
max = 18; Clear[g]; g[max + 1] = 1; g[k_] := g[k] = 1 - 1/(1 - x^(k + 1))/(k + 1)/(1 - x/(x - 1/g[k + 1])); b[x_] := (1 - g[0])/(1 - x); CoefficientList[ Series[b[x], {x, 0, max}], x]*Range[1, max + 1]! (* Jean-François Alcover, Jan 24 2013, after Sergei N. Gladkovskii *)

Crossrefs

Sequence in context: A002873 A309910 A042171 * A189815 A143599 A264409

Adjacent sequences: A133145 A133146 A133147 * A133149 A133150 A133151

Keyword

easy,nonn

Author

Vladeta Jovovic, Sep 22 2007

Extensions

More terms from R. J. Mathar, Sep 28 2007

Status

approved