0,5

Row sums are:

{1, 2, 233, 21254, 11051042, 6201705512, 9567444441557, 17238867197795882,

59632628341248852482, 246097301765634903409022, 1592452784095853202164877422,...}.

i=9;

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, 231, 1},

{1, 10626, 10626, 1},

{1, 230230, 10590580, 230230, 1},

{1, 3108105, 3097744650, 3097744650, 3108105, 1},

{1, 30045015, 404255676825, 8758872997875, 404255676825, 30045015, 1},

{1, 225792840, 29367745734600, 8590065627370500, 8590065627370500, 29367745734600, 225792840, 1},

{1, 1391975640, 1360597978209600, 3847090783387644000, 51935725575733194000, 3847090783387644000, 1360597978209600, 1391975640, 1},

{1, 7307872110, 44036276871668400, 935730850543979256000, 122112875995989292908000, 122112875995989292908000, 935730850543979256000, 44036276871668400, 7307872110, 1},

{1, 33578000610, 1062267247477844100, 139153974370319068974000, 136472097773363828735592000, 1319230278475850344444056000, 136472097773363828735592000, 139153974370319068974000, 1062267247477844100, 33578000610, 1}

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}]

A0086645

Sequence in context: A122269 A140077 A051183 this_sequence A031965 A088289 A046009

Adjacent sequences: A156739 A156740 A156741 this_sequence A156743 A156744 A156745

nonn,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 14 2009