%I M4421 N1868 #19 Dec 20 2021 20:56:57
%S 1,-7,37,-199,40321,-5512813,136601407,-32373535937,4039314145093,
%T -377880467185583,123905113265594071,-53834048464836263969,
%U 66351862106782030159,-194322297839115779164331,149128127842572749235559291,-25454412383565669030714950177
%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 H. E. Salzer, <a href="https://doi.org/10.1002/sapm194928154">Coefficients for repeated integration with central differences</a>, Journal of Mathematics and Physics, 28 (1949), 54-61.
%F a(n) is the numerator of -(n/2)*M(n) - (2n+2)*M(n+1), where M(n) = (2/(2n+1)!)*Integral_{t=0..1} t*Product_{k=1..n} (t^2 - k^2). - _Emeric Deutsch_, Jan 25 2005
%p M:=n->(2/(2*n+1)!)*int(t*product(t^2-k^2,k=1..n),t=0..1): B:=n->-(n/2)*M(n)-(2*n+2)*M(n+1): seq(numer(B(n)),n=0..16); # _Emeric Deutsch_, Jan 25 2005
%Y Cf. A002195, A002196, A002684.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Emeric Deutsch_, Jan 25 2005