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A156740 A higher order odd Narayana-Riordan triangle sequence:i=7; q-factorial odd product: f(n)=Product[2*k - 1, {k, 0, n}]; Narayana combinations: a(n,m)-=Binomial[n, m]*f[n]/(f[m]*f[n - m]); General product form: t[n,m,i] = Product[a(n + k, m + k)/a(n - m + k, k), {k, 0, i}] 1
1, 1, 1, 1, 153, 1, 1, 4845, 4845, 1, 1, 74613, 2362745, 74613, 1, 1, 735471, 358664691, 358664691, 735471, 1, 1, 5311735, 25533510145, 393216056233, 25533510145, 5311735, 1, 1, 30421755, 1056158828725, 160324910200455, 160324910200455 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 155, 9692, 2511973, 718800326, 444293699995, 322762198901872,

375936459278442977, 517934214393739253282, 977731835276897269439162,...}.

LINKS

Table of n, a(n) for n=0..32.

FORMULA

i=7;

q-factorial odd product:

f(n)=Product[2*k - 1, {k, 0, n}];

Narayana combinations:

a(n,m)-=Binomial[n, m]*f[n]/(f[m]*f[n - m]);

General product form:

t[n,m,i] = Product[a(n + k, m + k)/a(n - m + k, k), {k, 0, i}]

EXAMPLE

{1},

{1, 1},

{1, 153, 1},

{1, 4845, 4845, 1},

{1, 74613, 2362745, 74613, 1},

{1, 735471, 358664691, 358664691, 735471, 1},

{1, 5311735, 25533510145, 393216056233, 25533510145, 5311735, 1},

{1, 30421755, 1056158828725, 160324910200455, 160324910200455, 1056158828725, 30421755, 1},

{1, 145422675, 28915117583625, 31700607244180875, 312477414264068625, 31700607244180875, 28915117583625, 145422675, 1},

{1, 601080390, 571311883685250, 3587267317659684750, 255379268566725176250, 255379268566725176250, 3587267317659684750, 571311883685250, 601080390, 1},

{1, 2203961430, 8658548992740900, 259886348017118113500, 105962751896070430822500, 765286541471619778162500, 105962751896070430822500, 259886348017118113500, 8658548992740900, 2203961430, 1}

MATHEMATICA

Clear[t, n, m, i, A, f];

f[n_] = Product[2*k - 1, {k, 0, n}];

A[n_, m_] = Binomial[n, m]*f[n]/(f[m]*f[n - m]);

t[n_, m_, i_] = Product[A[n + k, m + k]/A[n - m + k, k], {k, 0, i}];

Table[Flatten[Table[Table[t[n, m, i], {m, 0, n}], {n, 0, 10}]], {i, 6, 9}]

CROSSREFS

Cf. A0086645

Row sums are in A151614.

Sequence in context: A157881 A099117 A109778 * A095226 A165340 A183985

Adjacent sequences:  A156737 A156738 A156739 * A156741 A156742 A156743

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 14 2009

STATUS

approved

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Last modified March 27 12:31 EDT 2017. Contains 284176 sequences.