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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

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

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.

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); (Deutsch)

CROSSREFS

Cf. A002195, A002196, A002684.

Sequence in context: A117130 A002807 A124610 * A126475 A274674 A255672

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 December 7 05:39 EST 2016. Contains 278841 sequences.