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A172349 Triangle t(n,k) read by rows: fibonomial ratios c(n)/(c(k)*c(n-k)) where c are partial products of a generalized Fibonacci sequence with multiplier m=4. 2
1, 1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 9, 45, 9, 1, 1, 29, 261, 261, 29, 1, 1, 65, 1885, 3393, 1885, 65, 1, 1, 181, 11765, 68237, 68237, 11765, 181, 1, 1, 441, 79821, 1037673, 3343613, 1037673, 79821, 441, 1, 1, 1165, 513765, 18598293, 134321005, 134321005 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Start from the generalized Fibonacci sequence A006131 and its partial products c(n) = 1, 1, 1, 5, 45, 1305, 84825, 15353325, 6770816325, 7888001018625... Then t(n,k) = c(n)/(c(k)*c(n-k)).

Row sums are 1, 2, 3, 12, 65, 582, 7295, 160368, 5579485, 306868458, 26280601275,...

LINKS

Table of n, a(n) for n=0..50.

EXAMPLE

1;

1, 1;

1, 1, 1;

1, 5, 5, 1;

1, 9, 45, 9, 1;

1, 29, 261, 261, 29, 1;

1, 65, 1885, 3393, 1885, 65, 1;

1, 181, 11765, 68237, 68237, 11765, 181, 1;

1, 441, 79821, 1037673, 3343613, 1037673, 79821, 441, 1;

1, 1165, 513765, 18598293, 134321005, 134321005, 18598293, 513765, 1165, 1;

1, 2929, 3412285, 300963537, 6052711133, 13566421505, 6052711133, 300963537, 3412285, 2929, 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

Cf. A010048 (m=1), A015109 (m=2), A172347 (m=3), A172350 (m=5).

Sequence in context: A178916 A046568 A046571 * A144403 A188587 A174119

Adjacent sequences:  A172346 A172347 A172348 * A172350 A172351 A172352

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula and Gary W. Adamson, Feb 01 2010

STATUS

approved

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Last modified December 11 21:15 EST 2017. Contains 295919 sequences.