The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A228836 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A228836

Triangle defined by T(n,k) = binomial(n^2, (n-k)*k), for n>=0, k=0..n, as read by rows.
(history; published version)

#11 by Paul D. Hanna at Sun Sep 08 17:32:40 EDT 2013

STATUS

editing

approved

#10 by Paul D. Hanna at Sun Sep 08 17:32:37 EDT 2013

CROSSREFS

Cf. related triangles: A228900(exp), A209330, A226234, A228832.

STATUS

approved

editing

#9 by Paul D. Hanna at Thu Sep 05 07:26:58 EDT 2013

STATUS

editing

approved

#8 by Paul D. Hanna at Thu Sep 05 07:26:55 EDT 2013

LINKS

Paul D. Hanna, <a href="/A228836/b228836.txt">Table Rows 0..30 as a flattened table of n, a(n) for n = 0..495</a>

#7 by Paul D. Hanna at Thu Sep 05 07:26:31 EDT 2013

LINKS

Paul D. Hanna, <a href="/A228836/b228836.txt">Table of n, a(n) for n = 0..495</a>

STATUS

approved

editing

#6 by Paul D. Hanna at Thu Sep 05 01:55:08 EDT 2013

STATUS

editing

approved

#5 by Paul D. Hanna at Thu Sep 05 01:55:05 EDT 2013

NAME

Triangle defined by T(n,k) = binomial(n^2, (n-k)*k), for n>=0, k=0..n, as read by rows.

EXAMPLE

The triangle of coefficients C(n^2, (n-k)*k), n>=k, k=0..n, begins:

PROG

(PARI) {T(n, k)=binomial(n^2, (n-k)*k)}

CROSSREFS

Cf. A207136 (row sums), A228837 (antidiagonal sums), A070780 (column 1).

STATUS

approved

editing

#4 by Paul D. Hanna at Thu Sep 05 01:52:57 EDT 2013

STATUS

editing

approved

#3 by Paul D. Hanna at Thu Sep 05 01:52:53 EDT 2013

NAME

allocated Triangle defined by T(n,k) = binomial(n^2, (n-k)*k), for Paul Dn>=0, k=0..n, as read by rows. Hanna

DATA

1, 1, 1, 1, 4, 1, 1, 36, 36, 1, 1, 560, 1820, 560, 1, 1, 12650, 177100, 177100, 12650, 1, 1, 376992, 30260340, 94143280, 30260340, 376992, 1, 1, 13983816, 8217822536, 92263734836, 92263734836, 8217822536, 13983816, 1, 1, 621216192, 3284214703056, 159518999862720, 488526937079580

OFFSET

0,5

EXAMPLE

The triangle of coefficients C(n^2, (n-k)*k), n>=k, k=0..n, begins:

1;

1, 1;

1, 4, 1;

1, 36, 36, 1;

1, 560, 1820, 560, 1;

1, 12650, 177100, 177100, 12650, 1;

1, 376992, 30260340, 94143280, 30260340, 376992, 1;

1, 13983816, 8217822536, 92263734836, 92263734836, 8217822536, 13983816, 1;

1, 621216192, 3284214703056, 159518999862720, 488526937079580, 159518999862720, 3284214703056, 621216192, 1; ...

PROG

(PARI) {T(n, k)=binomial(n^2, (n-k)*k)}

for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))

CROSSREFS

Cf. A207136 (row sums), A228837 (antidiagonal sums).

Cf. related triangles: A209330, A226234, A228832.

KEYWORD

allocated

nonn,tabl

AUTHOR

Paul D. Hanna, Sep 05 2013

STATUS

approved

editing

#2 by Paul D. Hanna at Thu Sep 05 01:48:46 EDT 2013

KEYWORD

allocating

allocated