A128061 a(n) = numerator of b(n), where sum{m>=0} b(m)*x^m/m! = x/(sum{m>=1} H(m) x^m/m!) = exp(-x)*x/(sum{m>=1} x^m (-1)^(m+1)/(m!*m)). (H(m) = sum{k=1 to m} 1/k.).

1, -3, 37, -29, 2761, -97, -268271, 14759, 2804929, -9435089, 3731508001, 1185970223, -264025807957621, 44820288709817, 4570382525453089, -336032650312339, 23787999916667875201, 4316502548043120587, -4994567510209019657318207

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

b(0)=1. b(n) = -sum{k=1 to n} binomial(n,k) H(k+1) b(n-k)/(k+1).

Example

1/(1 + x * 3/(2 * 2) + x^2 * 11/(6 * 6) + x^3 * 25/(12 * 24) +...) = 1 -x * 3/4 + x^2 * 37/72 -x^3 * 29/96 ...

Mathematica

b[0] = 1; b[n_] := b[n] = -Sum[Binomial[n, k] *HarmonicNumber[k + 1]*b[n - k]/(k + 1), {k, n}]; Numerator[Array[b, 20, 0]] (* Ray Chandler, Feb 19 2007 *)

Crossrefs

Cf. A128062.

Sequence in context: A372478 A002563 A140448 * A176240 A116184 A037000

Adjacent sequences: A128058 A128059 A128060 * A128062 A128063 A128064

Keyword

frac,sign

Author

Leroy Quet, Feb 13 2007

Extensions

Extended by Ray Chandler, Feb 19 2007

Status

approved