A002546 - OEIS

A002546

Denominator of Sum_{i+j+k=n; i,j,k > 0} 1/(i*j*k).
(Formerly M1110 N0424)

1, 2, 4, 8, 15, 240, 15120, 672, 8400, 100800, 69300, 4950, 17199000, 22422400, 33633600, 201801600, 467812800, 102918816000, 410646075840, 3555377280, 215100325440, 5162407810560, 30920671782000, 190281057120, 1085315579548200, 562756226432400, 22969641895200

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Denominators of coefficients for numerical differentiation.

REFERENCES

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.

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=1..27.

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) [Annotated scanned copy]

A. N. Lowan, H. E. Salzer and A. Hillman, A table of coefficients for numerical differentiation, Bull. Amer. Math. Soc., 48 (1942), 920-924. [Annotated scanned copy]

FORMULA

G.f.: (-log(1-x))^3 (for fractions A002545(n)/A002546(n)). - Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002

A002545(n)/A002546(n) = 6*Stirling_1(n+3, 3)(-1)^n/(n+3)!. - Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002

MAPLE

seq(denom(-Stirling1(j, 3)/j!*3!*(-1)^j), j=3..50); # Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002

MATHEMATICA

Denominator[Table[Sum[1/i/j/(n-i-j), {i, n-2}, {j, n-i-1}], {n, 3, 100}]] (* Ryan Propper *)

CROSSREFS

Cf. A002545.

Sequence in context: A371351 A026096 A098864 * A289089 A010745 A269266

Adjacent sequences: A002543 A002544 A002545 * A002547 A002548 A002549

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002

STATUS

approved