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A002683 Numerators of coefficients for repeated integration.
(Formerly M4421 N1868)
1
1, -7, 37, -199, 40321, -5512813, 136601407, -32373535937, 4039314145093, -377880467185583, 123905113265594071, -53834048464836263969, 66351862106782030159, -194322297839115779164331, 149128127842572749235559291, -25454412383565669030714950177 (list; graph; refs; listen; history; text; internal format)
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)!)*int(t*product(t^2-k^2, k=1..n), t=0..1). - 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 A126475 A274674

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

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Last modified July 16 12:12 EDT 2020. Contains 335788 sequences. (Running on oeis4.)