A002683 Numerators of coefficients for repeated integration.
1, -7, 37, -199, 40321, -5512813, 136601407, -32373535937, 4039314145093, -377880467185583, 123905113265594071, -53834048464836263969, 66351862106782030159, -194322297839115779164331, 149128127842572749235559291, -25454412383565669030714950177
Offset: 0
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
- H. E. Salzer, Coefficients for repeated integration with central differences, Journal of Mathematics and Physics, 28 (1949), 54-61.
Programs
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Maple
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
Formula
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
Extensions
More terms from Emeric Deutsch, Jan 25 2005