

A100645


Numerator of Cotesian number C(n,2).


2



1, 3, 2, 25, 9, 49, 464, 27, 16175, 3237113, 105387, 1737125143, 770720657, 25881785, 1997012608, 135505859252213, 214182958293, 528114253960241, 19467909708875, 595278405326437, 66462260889140083, 180690496141440384775397, 1610254561193224
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OFFSET

2,2


REFERENCES

Charles Jordan, Calculus of Finite Differences, Chelsea 1965, p. 513.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 2..100


EXAMPLE

1/6, 3/8, 2/15, 25/144, 9/280, 49/640, 464/14175, 27/2240, 16175/199584, 3237113/87091200, 105387/875875, 1737125143/22353408000, 770720657/5003856000, 25881785/229605376, ... = A100645/A100646 = A002179/A002176 (the latter not being in lowest terms)


MATHEMATICA

cn[n_, 0] := Sum[n^j*StirlingS1[n, j]/(j+1), {j, 1, n+1}]/n!; cn[n_, n_] := cn[n, 0]; cn[n_, k_] := 1/n!*Binomial[n, k]*Sum[n^(j+m)*StirlingS1[k, j]* StirlingS1[nk, m]/((m+1)*Binomial[j+m+1, m+1]), {m, 1, n}, {j, 1, k+1}]; a[n_] := Numerator[cn[n, 2]]; Table[a[n], {n, 2, 24}] (* JeanFrançois Alcover, Oct 08 2013 *)


CROSSREFS

Cf. A100646.
See A002176 for further references. A diagonal of A100640/A100641.
Sequence in context: A228772 A165714 A090883 * A132960 A009574 A059422
Adjacent sequences: A100642 A100643 A100644 * A100646 A100647 A100648


KEYWORD

sign,frac


AUTHOR

N. J. A. Sloane, Dec 05 2004


STATUS

approved



