|
%I M5136 N2227 #20 Oct 04 2021 12:36:06
%S 1,-1,1,-23,263,-133787,157009,-16215071,2689453969,-26893118531,
%T 5600751928169,-3340626516019229,885646796787371,-859202038021848149,
%U 2766671664340938282413,-319473088311274492668499,436677987276721765221113,-191960665849028069896950959123
%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+1)/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): A:=n->((n+1)/2)*M(n)+(2*n+2)*M(n+1): seq(numer(A(n)),n=0..18); # _Emeric Deutsch_, Jan 25 2005
%t M[n_] := (2/(2n+1)!) Integrate[t Product[t^2-k^2, {k, 1, n}], {t, 0, 1}];
%t A[n_] := ((n+1)/2) M[n] + (2n+2) M[n+1];
%t Table[Numerator[A[n]], {n, 0, 18}] (* _Jean-François Alcover_, Oct 04 2021, after Maple code *)
%Y Cf. A002195, A002196, A002682.
%K sign,frac
%O 0,4
%A _N. J. A. Sloane_
%E More terms from _Emeric Deutsch_, Jan 25 2005
|
