A002684 Denominators of coefficients for repeated integration.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac

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.

Crossrefs

Cf. A002195, A002196, A002683.

Programs

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

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

Extensions

More terms from Emeric Deutsch, Jan 25 2005