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A156003 Triangle read by rows: t0(n,m)=Binomial[3*n, m - 1]; t(n,m)=t0(n,m)+t0(n,n-m+1) 0
2, 7, 7, 37, 18, 37, 221, 78, 78, 221, 1366, 470, 210, 470, 1366, 8569, 3078, 969, 969, 3078, 8569, 54265, 20370, 6195, 2660, 6195, 20370, 54265, 346105, 134620, 42780, 12650, 12650, 42780, 134620, 346105, 2220076, 888057, 296361, 83655, 35100 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row sums are: 2, 14, 92, 598, 3882, 25232, 164320, 1072310, 7011398, 45928174, ....

LINKS

Table of n, a(n) for n=1..41.

B. Brainerd and T. V. Narayana, A Note on Simple Binomial Sampling Plans, Ann. Math. Statist. Volume 32, Number 3 (1961), 906-908.

FORMULA

t0(n,m)=Binomial[3*n, m - 1]; t(n,m)=t0(n,m)+t0(n,n-m+1).

EXAMPLE

{2},

{7, 7},

{37, 18, 37},

{221, 78, 78, 221},

{1366, 470, 210, 470, 1366},

{8569, 3078, 969, 969, 3078, 8569},

{54265, 20370, 6195, 2660, 6195, 20370, 54265},

{346105, 134620, 42780, 12650, 12650, 42780, 134620, 346105},

{2220076, 888057, 296361, 83655, 35100, 83655, 296361, 888057, 2220076},

{14307151, 5852955, 2036235, 597835, 169911, 169911, 597835, 2036235, 5852955, 14307151}

MATHEMATICA

a[n_, m_] = Binomial[3*n, m - 1];

Table[Table[a[n, m] + a[n, n - m + 1], {m, 1, n}], {n, 1, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A090521 A090523 A164314 * A306417 A011416 A086658

Adjacent sequences:  A156000 A156001 A156002 * A156004 A156005 A156006

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 01 2009

STATUS

approved

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Last modified July 24 02:42 EDT 2019. Contains 325287 sequences. (Running on oeis4.)