|
Search: id:A002546
|
|
|
| A002546 |
|
Denominator of sum 1/(i*j*k) for i,j,k>0 and i+j+k=n.
(Formerly M1110 N0424)
|
|
+0
2
|
|
| 1, 2, 4, 8, 15, 240, 15120, 672, 8400, 100800, 69300, 4950, 17199000, 22422400, 33633600, 201801600, 467812800, 102918816000, 410646075840, 3555377280, 215100325440, 5162407810560, 30920671782000, 190281057120
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Denominators of coefficients for numerical differentiation.
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
W. G. Bickley and J. C. P. Miller, Numerical differentiation near the limits of a difference table, Phil. Mag., 33 (1942), 1-12 (plus tables).
A. N. Lowan, H. E. Salzer and A. Hillman, A table of coefficients for numerical differentiation, Bull. Amer. Math. Soc., 48 (1942), 920-924.
|
|
FORMULA
|
G.f.: (-ln(1-x))^3 (for fractions A002545(n)/A002546(n))
A002545(n)/A002546(n)=6 stirling1(n+3, n)(-1)^n/(n+3)!
|
|
MAPLE
|
with(combinat):seq(denom(stirling1(j+3, 3)/(j+3)!*3!*(-1)^j), j=0..50);
|
|
MATHEMATICA
|
Denominator[Table[Sum[1/i/j/(n-i-j), {i, n-2}, {j, n-i-1}], {n, 3, 100}]] (Propper)
|
|
CROSSREFS
|
Cf. A002545.
Sequence in context: A007673 A026096 A098864 this_sequence A010745 A097777 A089738
Adjacent sequences: A002543 A002544 A002545 this_sequence A002547 A002548 A002549
|
|
KEYWORD
|
nonn,frac
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms, GF, formula, Maple code from Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19, 2002
|
|
|
Search completed in 0.002 seconds
|
