

A165507


Triangle T(n,m) read by rows: numerator of 1/(1+nm)^2  1/m^2.


3



0, 3, 3, 8, 0, 8, 15, 5, 5, 15, 24, 3, 0, 3, 24, 35, 21, 7, 7, 21, 35, 48, 2, 16, 0, 16, 2, 48, 63, 45, 1, 9, 9, 1, 45, 63, 80, 15, 40, 5, 0, 5, 40, 15, 80, 99, 77, 55, 33, 11, 11, 33, 55, 77, 99, 120, 6, 8, 3, 24, 0, 24, 3, 8, 6, 120
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OFFSET

1,2


COMMENTS

The triangle is obtained from the infinite array shown in the comment in A172370 by starting in column 1 and reading diagonally upwards along increasing columns or starting in column 1 and reading diagonally upwards along decreasing columns.
Equivalence of these two interpretations follows from the mirror symmetry m <> m along column m=0 in that array.
T(n,m) is antisymmetric (changes sign) with respect to a central zero if the row index n is odd, and with respect to the separator in the middle of the row if the row index n is even: T(n,m) = T(n,n+1m).
An appropriate triangle of denominators is in A143183.


LINKS

G. C. Greubel, Rows n=1..100 of triangle, flattened


FORMULA

T(n,m) = A173651(1+n,m), m>=1.


EXAMPLE

The triangle starts in row n=1 with columns 1<=m<=n as
0;
3,3;
8,0,8;
15,5,5,15;
24,3,0,3,24;
35,21,7,7,21,35;
48,2,16,0,16,2,48;


MAPLE

A165507 := proc(n, m) 1/(1+nm)^21/m^2 ; numer(%) ; end proc:


MATHEMATICA

Table[Numerator[1/(nk+1)^2  1/k^2], {n, 1, 15}, {k, 1, n}]//Flatten (* G. C. Greubel, Oct 21 2018 *)


PROG

(PARI) for(n=1, 15, for(k=1, n, print1(numerator(1/(nk+1)^2  1/k^2), ", "))) \\ G. C. Greubel, Oct 21 2018
(MAGMA) [[Numerator(1/(nk+1)^2  1/k^2): k in [1..n]]: n in [1..15]]; // G. C. Greubel, Oct 21 2018


CROSSREFS

Cf. A120072, A143183, A165441.
Sequence in context: A248859 A171543 A079073 * A212636 A282255 A164040
Adjacent sequences: A165504 A165505 A165506 * A165508 A165509 A165510


KEYWORD

sign,frac,tabl,easy


AUTHOR

Paul Curtz, Sep 21 2009


STATUS

approved



