%I A156917
%S A156917 1,1,1,1,40,1,1,1210,1210,1,1,33880,1024870,33880,1,1,925771,784128037,
%T A156917 784128037,925771,1,1,25095280,580812061522,16262737722616,580812061522,
%U A156917 25095280,1,1,678468820,425659125229240,325671796712891524
%N A156917 General q-Narayana triangle sequence: q=3;m=2; c(n,l,m)=Product[q-binomial(n 
               + k, l + k, m)/q-binomial(n - l + k, k, m), {k, 0, m}]
%C A156917 Row sums are:
%C A156917 {1, 2, 42, 2422, 1092632, 1570107618, 17424412036222, 652194913033179170,
%C A156917 189060566695044668933610, 188602075109681827520528645944,
%C A156917 1459625430842679382287597833052615968 ,...}.
%C A156917 I have made the general Narayana level i equal to the m =q-1 q-combination 
               / Gaussian level,
%C A156917 but that is not necessary.
%F A156917 q=3;m=2;
%F A156917 c(n,l,m)=Product[q-binomial(n + k, l + k, m)/q-binomial(n - l + k, k, 
               m), {k, 0, m}]
%e A156917 {1},
%e A156917 {1, 1},
%e A156917 {1, 40, 1},
%e A156917 {1, 1210, 1210, 1},
%e A156917 {1, 33880, 1024870, 33880, 1},
%e A156917 {1, 925771, 784128037, 784128037, 925771, 1},
%e A156917 {1, 25095280, 580812061522, 16262737722616, 580812061522, 25095280, 1},
%e A156917 {1, 678468820, 425659125229240, 325671796712891524, 325671796712891524, 
               425659125229240, 678468820, 1},
%e A156917 {1, 18326727760, 310852833944711080, 6447056947633081877440, 176165831094073962301048, 
               6447056947633081877440, 310852833944711080, 18326727760, 1},
%e A156917 {1, 494894285941, 226744821210507560554, 127139910155209947281116468, 
               94173897417940882107581360008, 94173897417940882107581360008, 127139910155209947281116468, 
               226744821210507560554, 494894285941, 1},
%e A156917 {1, 13362799477720, 165329327642475178468363, 2504087254915277031691820226328, 
               50145960006476009671341554681490292, 1359328502654886873735539664093290560, 
               50145960006476009671341554681490292, 2504087254915277031691820226328, 
               165329327642475178468363, 13362799477720, 1}
%t A156917 Clear[t, n, m, i, k, c, b];
%t A156917 t[n_, m_] = If[m == 0, n!, Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 
               1, n}]];
%t A156917 b[n_, k_, m_] = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])]
%t A156917 c[n_, l_, m_] = Product[b[n + k, l + k, m]/b[n - l + k, k, m], {k, 0, 
               m}]
%t A156917 Table[Flatten[Table[Table[c[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 
               10}]
%Y A156917 A001263
%Y A156917 Sequence in context: A013375 A013419 A013420 this_sequence A078084 A037937 
               A126652
%Y A156917 Adjacent sequences: A156914 A156915 A156916 this_sequence A156918 A156919 
               A156920
%K A156917 nonn,tabl,uned
%O A156917 0,5
%A A156917 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 18 2009