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A323855 Triangle read by rows: T(n,k) is the denominator of the generalized harmonic number H(n,k) of rank k (n >= 1, 0 <= k <= n - 1). 1
1, 2, 1, 6, 1, 1, 12, 12, 2, 1, 60, 4, 4, 1, 1, 20, 45, 8, 6, 2, 1, 140, 90, 120, 3, 3, 1, 1, 280, 5040, 80, 80, 2, 4, 2, 1, 2520, 1008, 378, 16, 144, 4, 12, 1, 1, 2520, 25200, 6048, 15120, 288, 240, 24, 3, 2, 1, 27720, 25200, 21600, 5040, 6048, 40, 240, 1, 2, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A323854 for the definition of H(n,k).

LINKS

Table of n, a(n) for n=1..66.

Gi-Sang Cheon and Moawwad E. A. El-Mikkawy, Generalized harmonic number identities and a related matrix representation, J. Korean Math. Soc, Volume 44, 2007, 487-498.

Gi-Sang Cheon and Moawwad E. A. El-Mikkawy, Generalized harmonic numbers with Riordan arrays, Journal of Number Theory, Volume 128, Issue 2, 2008, 413-425.

Joseph M. Santmyer, A Stirling like sequence of rational numbers, Discrete Math., Volume 171, no. 1-3, 1997, 229-235, MR1454453.

FORMULA

T(n,k) = denominator of H(n,k), where H(n,k) = ((1/n!)*(-1)^(r + 1))*(((d/dt)^n (1/t)*log(t)^(r + 1))_{t=1}).

EXAMPLE

Triangle T(n,k) begins:

  n\k |   0    1    2    3    4    5    6

  ---------------------------------------

    1 |   1

    2 |   2    1

    3 |   6    1    1

    4 |  12   12    2    1

    5 |  60    4    4    3    1

    6 |  20   45    8    6    2    1

    7 | 140   90  120    3    3    4    1

    ...

MATHEMATICA

H[n_, k_] := -(-1)^(n + k)/n!*(D[Log[t]^(k + 1)/t, {t, n}] /. t->1)

Table[Denominator[H[n, k]], {n, 1, 20}, {k, 0, n - 1}] // Flatten

PROG

(Maxima)

H(n, k) := -(-1)^(k + n)/n!*at(diff(log(t)^(k + 1)/t, t, n), t = 1)$

create_list(denom(H(n, k)), n, 1, 20, k, 0, n - 1);

CROSSREFS

Cf. A323854 (numerators), A002805 (Column 0).

Sequence in context: A089808 A290318 A139547 * A126342 A229818 A324500

Adjacent sequences:  A323852 A323853 A323854 * A323856 A323857 A323858

KEYWORD

nonn,easy,tabl,frac

AUTHOR

Franck Maminirina Ramaharo, Feb 01 2019

STATUS

approved

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Last modified June 1 07:40 EDT 2020. Contains 334759 sequences. (Running on oeis4.)