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 A173918 A double product sequence based on a=3;f(n,a)=f(n-1,a)+a*f(n-2,a) 0
 1, 1, 1, 1, 4, 1, 1, 28, 28, 1, 1, 133, 931, 133, 1, 1, 760, 25270, 25270, 760, 1, 1, 3880, 737200, 3501700, 737200, 3880, 1, 1, 21049, 20417530, 554190100, 554190100, 20417530, 21049, 1, 1, 110236, 580089391, 80383815610, 459336089200 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, 6, 58, 1199, 52062, 4983862, 1149257360, 621264119676, 736123531927540, 2029965262731727157,...}. I get these same sequences using a Narayana form: w[n_, m_, q_] := c[n - 1, q]*c[n, q]/(c[m - 1, q]*c[n - m, q]*c[m - 1, q]*c[n - m + 1, q]*f[m, q]) LINKS Table of n, a(n) for n=0..40. FORMULA c(n,a)=If[n == 0, 1, Product[f(i, a)*f(i + 1, a), {i, 1, n}]] EXAMPLE {1}, {1, 1}, {1, 4, 1}, {1, 28, 28, 1}, {1, 133, 931, 133, 1}, {1, 760, 25270, 25270, 760, 1}, {1, 3880, 737200, 3501700, 737200, 3880, 1}, {1, 21049, 20417530, 554190100, 554190100, 20417530, 21049, 1}, {1, 110236, 580089391, 80383815610, 459336089200, 80383815610, 580089391, 110236, 1}, {1, 588772, 16225967548, 12197871104209, 355847668303240, 355847668303240, 12197871104209, 16225967548, 588772, 1}, {1, 3109597, 457710911221, 1802007857477077, 285191454075451081, 1455977423437829203, 285191454075451081, 1802007857477077, 457710911221, 3109597, 1} MATHEMATICA Clear[t, n, m, c, q, w, f, a]; f[0, a_] := 0; f[1, a_] := 1; f[n_, a_] := f[n, a] = f[n - 1, a] + a*f[n - 2, a]; c[n_, a_] := If[n == 0, 1, Product[f[i, a]*f[i + 1, a], {i, 1, n}]]; w[n_, m_, q_] := c[n, q]/(c[m, q]*c[n - m, q]); Table[Table[Table[w[n, m, q], {m, 0, n}], {n, 0, 10}], {q, 1, 12}]; Table[Flatten[Table[Table[w[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 12}] CROSSREFS Sequence in context: A140805 A113370 A078536 * A174412 A177939 A209196 Adjacent sequences: A173915 A173916 A173917 * A173919 A173920 A173921 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Mar 02 2010 STATUS approved

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Last modified May 29 15:02 EDT 2023. Contains 363042 sequences. (Running on oeis4.)