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A176566 Triangle T(n,m) = binomial( n*(n+1)/2+m, m ) read by rows. 0
1, 1, 1, 1, 2, 3, 1, 4, 10, 20, 1, 7, 28, 84, 210, 1, 11, 66, 286, 1001, 3003, 1, 16, 136, 816, 3876, 15504, 54264, 1, 22, 253, 2024, 12650, 65780, 296010, 1184040, 1, 29, 435, 4495, 35960, 237336, 1344904, 6724520, 30260340, 1, 37, 703, 9139, 91390, 749398 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are A107868(n).

LINKS

Table of n, a(n) for n=0..50.

FORMULA

T(n,m)= binomial(binomial(n, 2) + m, m), 0<=m<=n.

EXAMPLE

1;

1, 1;

1, 2, 3;

1, 4, 10, 20;# A000292

1, 7, 28, 84, 210;# A000579

1, 11, 66, 286, 1001, 3003;# A001287

1, 16, 136, 816, 3876, 15504, 54264;# A010968

1, 22, 253, 2024, 12650, 65780, 296010, 1184040; # A010974

1, 29, 435, 4495, 35960, 237336, 1344904, 6724520, 30260340;

1, 37, 703, 9139, 91390, 749398, 5245786, 32224114, 177232627, 886163135;

1, 46, 1081, 17296, 211876, 2118760, 18009460, 133784560, 886322710, 5317936260, 29248649430;

MATHEMATICA

t[n_, m_] = Binomial[Binomial[n, 2] + m, m];

Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Cf. A158498.

Sequence in context: A211233 A084608 A078990 * A079639 A104694 A125182

Adjacent sequences:  A176563 A176564 A176565 * A176567 A176568 A176569

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Apr 20 2010

STATUS

approved

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Last modified February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)