A002684 Denominators of coefficients for repeated integration. (Formerly M4307 N1802)

6, 360, 10080, 259200, 239500800, 145297152000, 15692092416000, 16005934264320000, 8515157028618240000, 3372002183332823040000, 4653363012999295795200000, 8469120683658718347264000000

Offset

0,1

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..11.

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

Formula

a(n) is the denominator 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(denom(B(n)), n=0..13); # Emeric Deutsch, Jan 25 2005

Crossrefs

Cf. A002195, A002196, A002683.

Sequence in context: A233463 A290782 A367519 * A036281 A202367 A262179

Adjacent sequences: A002681 A002682 A002683 * A002685 A002686 A002687

Keyword

nonn,frac

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, Jan 25 2005

Status

approved