OFFSET
0,8
COMMENTS
Start from the generalized Fibonacci sequence A015442 and its partial products c(n) = 1, 1, 1, 8, 120, 8520, 1499520, 1009176960, 1922482108800... Then t(n,k) = c(n)/(c(k)*c(n-k)).
Row sums are 1, 2, 3, 18, 152, 2274, 48776, 2340696, 192484504, 27026705688, 6379354108992,...
EXAMPLE
1;
1, 1;
1, 1, 1;
1, 8, 8, 1;
1, 15, 120, 15, 1;
1, 71, 1065, 1065, 71, 1;
1, 176, 12496, 23430, 12496, 176, 1;
1, 673, 118448, 1051226, 1051226, 118448, 673, 1;
1, 1905, 1282065, 28205430, 133505702, 28205430, 1282065, 1905, 1;
1, 6616, 12603480, 1060267755, 12440474992, 12440474992, 1060267755, 12603480, 6616, 1;
MATHEMATICA
Clear[f, c, a, t];
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], {i, 1, n}]];
t[n_, m_, a_] := c[n, a]/(c[m, a]*c[n - m, a]);
Table[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}], {a, 1, 10}];
Table[Flatten[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}]], {a, 1, 10}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula and Gary W. Adamson, Feb 01 2010
STATUS
approved