A002683 Numerators of coefficients for repeated integration. (Formerly M4421 N1868)

1, -7, 37, -199, 40321, -5512813, 136601407, -32373535937, 4039314145093, -377880467185583, 123905113265594071, -53834048464836263969, 66351862106782030159, -194322297839115779164331, 149128127842572749235559291, -25454412383565669030714950177

Offset

0,2

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

Table of n, a(n) for n=0..15.

H. E. Salzer, Coefficients for repeated integration with central differences, Journal of Mathematics and Physics, 28 (1949), 54-61.

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

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

Crossrefs

Cf. A002195, A002196, A002684.

Sequence in context: A117130 A002807 A124610 * A319013 A362247 A126475

Adjacent sequences: A002680 A002681 A002682 * A002684 A002685 A002686

Keyword

sign,frac

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, Jan 25 2005

Status

approved