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 A174411 A product triangle sequence based on:a=1;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}]]; t(n,m,a)=If[Floor[n/2] >= m, c(n, a)/c(n - m, a), c(n, a)/c(m, a)] 0
 1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 15, 90, 15, 1, 1, 40, 600, 600, 40, 1, 1, 104, 4160, 62400, 4160, 104, 1, 1, 273, 28392, 1135680, 1135680, 28392, 273, 1, 1, 714, 194922, 20271888, 810875520, 20271888, 194922, 714, 1, 1, 1870, 1335180, 364504140 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, 4, 14, 122, 1282, 70930, 2328692, 851810570, 76548543502, 189143352851092,...} LINKS FORMULA a=1; 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}]]; t(n,m,a)=If[Floor[n/2] >= m, c(n, a)/c(n - m, a), c(n, a)/c(m, a)] EXAMPLE {1}, {1, 1}, {1, 2, 1}, {1, 6, 6, 1}, {1, 15, 90, 15, 1}, {1, 40, 600, 600, 40, 1}, {1, 104, 4160, 62400, 4160, 104, 1}, {1, 273, 28392, 1135680, 1135680, 28392, 273, 1}, {1, 714, 194922, 20271888, 810875520, 20271888, 194922, 714, 1}, {1, 1870, 1335180, 364504140, 37908430560, 37908430560, 364504140, 1335180, 1870, 1}, {1, 4895, 9153650, 6535706100, 1784247765300, 185561767591200, 1784247765300, 6535706100, 9153650, 4895, 1} MATHEMATICA 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}]]; t[n_, m_, q_] = If[Floor[n/2] >= m, c[n, q]/c[n - m, q], c[n, q]/c[m, q]]; Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}] CROSSREFS Sequence in context: A173881 A329228 A172373 * A322620 A155795 A009963 Adjacent sequences:  A174408 A174409 A174410 * A174412 A174413 A174414 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Mar 19 2010 STATUS approved

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Last modified August 12 07:38 EDT 2020. Contains 336438 sequences. (Running on oeis4.)