A002682 Denominators of coefficients for repeated integration. (Formerly M3152 N1277)

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

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..12.

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+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

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 *)

Crossrefs

Cf. A002195, A002196, A002681.

Sequence in context: A289193 A062346 A359860 * A073595 A370954 A117972

Adjacent sequences: A002679 A002680 A002681 * A002683 A002684 A002685

Keyword

nonn,frac

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, Jan 25 2005

Status

approved