A002689 Denominators of coefficients for repeated integration. (Formerly M4072 N1687)

2, 6, 8, 180, 32, 10080, 3456, 453600, 115200, 47900160, 71680, 217945728000, 36578304000, 2241727488000, 45984153600, 2000741783040000, 918421504, 43667471941632000, 5751865147392000, 240857298809487360000

Offset

0,1

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

H. E. Salzer, Table of coefficients for repeated integration with differences, Phil. Mag., 38 (1947), 331-336.

H. E. Salzer, Table of coefficients for repeated integration with differences, Phil. Mag., 38 (1947), 331-336. [Annotated scanned copy]

Formula

a(n) = A002207(n)/(n+1).

Maple

seq(denom(int(mul(p-i, i=0..(n-1)), p=0..1)/(n-1)!), n=1..30);

Mathematica

max = 19; a[n_] := Denominator[Sum[BernoulliB[j]/j*StirlingS1[n, j-1], {j, 1, n+1}]*(n+1)/n!]; Table[a[n], {n, 0, max}] (* or *)
a[n_] := Denominator[SeriesCoefficient[1/x - 1/Log[1+x], {x, 0, n}]] /(n+1); Table[a[n], {n, 0, max}] (* Jean-François Alcover, Apr 09 2014, after Paul Curtz *)

Crossrefs

Sequence in context: A124675 A279258 A120709 * A174727 A046728 A110984

Adjacent sequences: A002686 A002687 A002688 * A002690 A002691 A002692

Keyword

nonn,frac

Author

N. J. A. Sloane

Extensions

Corrected and edited by Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 01 2010

Status

approved