A128062 a(n) = denominator 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, 4, 72, 96, 21600, 17280, 5080320, 322560, 326592000, 145152000, 63228211200, 22992076800, 1298164008960000, 292919058432000, 11298306539520000, 273898340352000, 48978158848819200000, 886482513100800000

Offset

0,2

Links

Table of n, a(n) for n=0..17.

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}]; Denominator[Array[b, 20, 0]] (* Ray Chandler, Feb 19 2007 *)

Crossrefs

Cf. A128061.

Sequence in context: A340917 A161791 A132097 * A336253 A227248 A113839

Adjacent sequences: A128059 A128060 A128061 * A128063 A128064 A128065

Keyword

frac,nonn

Author

Leroy Quet, Feb 13 2007

Extensions

Extended by Ray Chandler, Feb 19 2007

Status

approved