A002688 Denominators of coefficients for repeated integration. (Formerly M4158 N1728)

6, 24, 45, 480, 10080, 24192, 907200, 1036800, 239500800, 106444800, 9906624000, 475517952000, 15692092416000, 4828336128000, 8002967132160000, 4268249137152000, 51607012294656000, 1202139815804928000

Offset

1,1

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

Michael De Vlieger, Table of n, a(n) for n = 1..442

Caroline Moosmüller and Tomas Sauer, Polynomial overreproduction by Hermite subdivision operators, and p-Cauchy numbers, arXiv:1904.10835 [math.NA], 2019.

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) = denominator((1/n!) * Sum_{k=1..n} Stirling1(n,k)/((k+1)*(k+2))). - Vladimir Kruchinin, Apr 06 2016

Maple

seq(denom(int(int(mul(p-i, i=0..(n-1)), p=0..p), p=0..1)/n!), n=1..30); # Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 01 2010

Mathematica

Table[Denominator@ (Sum[StirlingS1[n, k]/((k + 1) (k + 2)), {k, n}]/n!), {n, 20}] (* Michael De Vlieger, Apr 06 2016 *)

Prog

(Maxima)
a(n):=denom(1/n!*(sum((stirling1(n, k))/((k+1)*(k+2)), k, 1, n))); /* Vladimir Kruchinin, Apr 06 2016 */

Crossrefs

Cf. A002687.

Sequence in context: A062768 A161333 A253770 * A362803 A083212 A120572

Adjacent sequences: A002685 A002686 A002687 * A002689 A002690 A002691

Keyword

nonn,frac

Author

N. J. A. Sloane

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 01 2010

Status

approved