A002682 Denominators of coefficients for repeated integration.

3, 45, 252, 28350, 1496880, 3405402000, 17513496000, 7815397590000, 5543722023840000, 235212205868640000, 206559082608278400000, 516914104227216696000000, 572581776990147724800000

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, A002681.

Programs

Maple

M:=n->(2/(2*n+1)!)*int(t*product(t^2-k^2,k=1..n),t=0..1): A:=n->((n+1)/2)*M(n)+(2*n+2)*M(n+1): seq(denom(A(n)),n=0..15); # Emeric Deutsch, Jan 25 2005

Mathematica

M[n_] := (2/(2n+1)!) Integrate[t Product[t^2-k^2, {k, 1, n}], {t, 0, 1}];
A[n_] := ((n+1)/2) M[n] + (2n+2) M[n+1];
Table[Denominator[A[n]], {n, 0, 15}] (* Jean-François Alcover, Oct 04 2021, after Maple code *)

Formula

a(n) is the denominator of ((n+1)/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

Extensions

More terms from Emeric Deutsch, Jan 25 2005