This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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}] 0
 1, 1, 1, 1, 40, 1, 1, 1210, 1210, 1, 1, 33880, 1024870, 33880, 1, 1, 925771, 784128037, 784128037, 925771, 1, 1, 25095280, 580812061522, 16262737722616, 580812061522, 25095280, 1, 1, 678468820, 425659125229240, 325671796712891524 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, 42, 2422, 1092632, 1570107618, 17424412036222, 652194913033179170, 189060566695044668933610, 188602075109681827520528645944, 1459625430842679382287597833052615968 ,...}. I have made the general Narayana level i equal to the m =q-1 q-combination / Gaussian level, but that is not necessary. LINKS FORMULA 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}] EXAMPLE {1}, {1, 1}, {1, 40, 1}, {1, 1210, 1210, 1}, {1, 33880, 1024870, 33880, 1}, {1, 925771, 784128037, 784128037, 925771, 1}, {1, 25095280, 580812061522, 16262737722616, 580812061522, 25095280, 1}, {1, 678468820, 425659125229240, 325671796712891524, 325671796712891524, 425659125229240, 678468820, 1}, {1, 18326727760, 310852833944711080, 6447056947633081877440, 176165831094073962301048, 6447056947633081877440, 310852833944711080, 18326727760, 1}, {1, 494894285941, 226744821210507560554, 127139910155209947281116468, 94173897417940882107581360008, 94173897417940882107581360008, 127139910155209947281116468, 226744821210507560554, 494894285941, 1}, {1, 13362799477720, 165329327642475178468363, 2504087254915277031691820226328, 50145960006476009671341554681490292, 1359328502654886873735539664093290560, 50145960006476009671341554681490292, 2504087254915277031691820226328, 165329327642475178468363, 13362799477720, 1} MATHEMATICA Clear[t, n, m, i, k, c, b]; t[n_, m_] = If[m == 0, n!, Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; b[n_, k_, m_] = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])] c[n_, l_, m_] = Product[b[n + k, l + k, m]/b[n - l + k, k, m], {k, 0, m}] Table[Flatten[Table[Table[c[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 10}] CROSSREFS Sequence in context: A013375 A013419 A013420 * A176644 A078084 A037937 Adjacent sequences:  A156914 A156915 A156916 * A156918 A156919 A156920 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Feb 18 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 19 02:36 EST 2018. Contains 318245 sequences. (Running on oeis4.)