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A123163 Triangle read by rows: binomial[(n-m)^2,m^2]. 1
1, 1, 0, 1, 1, 0, 1, 4, 0, 0, 1, 9, 1, 0, 0, 1, 16, 126, 0, 0, 0, 1, 25, 1820, 1, 0, 0, 0, 1, 36, 12650, 11440, 0, 0, 0, 0, 1, 49, 58905, 2042975, 1, 0, 0, 0, 0, 1, 64, 211876, 94143280, 2042975, 0, 0, 0, 0, 0, 1, 81, 635376, 2054455634, 7307872110, 1, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..65.

FORMULA

a(n,m) = (n^2 - 2*n*m + m^2)!/((m^2)!(n^2 - 2*n*m)!)

EXAMPLE

n\m | 0   1      2      3  4  5  6  7

----+---------------------------------

0   | 1;

1   | 1,  0;

2   | 1,  1,     0;

3   | 1,  4,     0,     0;

4   | 1,  9,     1,     0, 0;

5   | 1, 16,   126,     0, 0, 0;

6   | 1, 25,  1820,     1, 0, 0, 0;

7   | 1, 36, 12650, 11440, 0, 0, 0, 0;

MATHEMATICA

t[n_, m_] = (n^2 - 2*n*m + m^2)!/((m^2)!(n^2 - 2*n*m)!); a = Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[a]

Flatten[Table[Binomial[(n-m)^2, m^2], {n, 0, 10}, {m, 0, n}]] (* Harvey P. Dale, Aug 08 2012 *)

CROSSREFS

Cf. A011973, A123165.

Sequence in context: A254156 A046783 A134832 * A194794 A317448 A292900

Adjacent sequences:  A123160 A123161 A123162 * A123164 A123165 A123166

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Oct 02 2006

EXTENSIONS

Edited by N. J. A. Sloane, Oct 04 2006

STATUS

approved

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Last modified July 5 00:40 EDT 2020. Contains 335457 sequences. (Running on oeis4.)