A002687 Numerators of coefficients for repeated integration. (Formerly M4457 N1887)

1, -1, 1, -7, 107, -199, 6031, -5741, 1129981, -435569, 35661419, -1523489833, 45183033541, -12597680311, 19055094997949, -9331210633373, 104148936040729, -2250170748719203, 734854328394419537, -826511503463860961

Offset

1,4

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..446

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

Maple

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

Mathematica

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

Prog

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

Crossrefs

Cf. A002688.

Sequence in context: A075021 A138963 A141932 * A354572 A166547 A156204

Adjacent sequences: A002684 A002685 A002686 * A002688 A002689 A002690

Keyword

sign,frac

Author

N. J. A. Sloane

Extensions

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

Status

approved