%I M4457 N1887 #33 Oct 19 2023 08:48:00
%S 1,-1,1,-7,107,-199,6031,-5741,1129981,-435569,35661419,-1523489833,
%T 45183033541,-12597680311,19055094997949,-9331210633373,
%U 104148936040729,-2250170748719203,734854328394419537,-826511503463860961
%N Numerators of coefficients for repeated integration.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Michael De Vlieger, <a href="/A002687/b002687.txt">Table of n, a(n) for n = 1..446</a>
%H Caroline Moosmüller and Tomas Sauer, <a href="https://arxiv.org/abs/1904.10835">Polynomial overreproduction by Hermite subdivision operators, and p-Cauchy numbers</a>, arXiv:1904.10835 [math.NA], 2019.
%H H. E. Salzer, <a href="http://dx.doi.org/10.1080/14786444708521604">Table of coefficients for repeated integration with differences</a>, Phil. Mag., 38 (1947), 331-336.
%H H. E. Salzer, <a href="/A002206/a002206_1.pdf">Table of coefficients for repeated integration with differences</a>, Phil. Mag., 38 (1947), 331-336. [Annotated scanned copy]
%F a(n) = numerator((1/n!) * Sum_{k=1..n} Stirling1(n,k)/((k+1)*(k+2))). - _Vladimir Kruchinin_, Apr 06 2016
%p seq(numer(int(int(mul(p-i,i=0..(n-1)),p=0..p),p=0..1)/n!),n=1..30);
%t Table[Numerator@ (Sum[StirlingS1[n, k]/((k + 1) (k + 2)), {k, n}]/n!), {n, 20}] (* _Michael De Vlieger_, Apr 06 2016 *)
%o (Maxima)
%o a(n):=num(1/n!*(sum((stirling1(n,k))/((k+1)*(k+2)),k,1,n))); /* _Vladimir Kruchinin_, Apr 06 2016 */
%Y Cf. A002688.
%K sign,frac
%O 1,4
%A _N. J. A. Sloane_
%E Corrected and edited by Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 01 2010