A002689 Denominators of coefficients for repeated integration.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac

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]

Programs

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 *)

Formula

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

Extensions

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