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A172375 A beta integer combination triangle of a Narayana type: a=2:f(n, a) = a*f(n - 1, a) + a*f(n - 2, a);c(n,a)=If[n == 0, 1, Product[f(i, a), {i, 1, n}]];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)) 0
1, 1, 1, 1, 6, 1, 1, 48, 48, 1, 1, 352, 2816, 352, 1, 1, 2640, 154880, 154880, 2640, 1, 1, 19680, 8659200, 63500800, 8659200, 19680, 1, 1, 146944, 481976320, 26508697600, 26508697600, 481976320, 146944, 1, 1, 1096704, 26859012096, 11012194959360 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are:

{1, 2, 8, 98, 3522, 315042, 80858562, 53981641730, 104669572331522,

521363491264516610,...}

LINKS

Table of n, a(n) for n=1..40.

FORMULA

a=2:

f(n, a) = a*f(n - 1, a) + a*f(n - 2, a);

c(n,a)=If[n == 0, 1, Product[f(i, a), {i, 1, n}]];

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))

EXAMPLE

{1},

{1, 1},

{1, 6, 1},

{1, 48, 48, 1},

{1, 352, 2816, 352, 1},

{1, 2640, 154880, 154880, 2640, 1},

{1, 19680, 8659200, 63500800, 8659200, 19680, 1},

{1, 146944, 481976320, 26508697600, 26508697600, 481976320, 146944, 1},

{1, 1096704, 26859012096, 11012194959360, 82591462195200, 11012194959360, 26859012096, 1096704, 1},

{1, 8186112, 1496290295808, 4580643358900224, 256099605974876160, 256099605974876160, 4580643358900224, 1496290295808, 8186112, 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] = a*f[n - 1, a] + a*f[n - 2, a];

c[n_, a_] := If[n == 0, 1, Product[f[i, a], {i, 1, n}]];

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]);

Table[Table[Table[w[n, m, q], {m, 1, n}], {n, 1, 10}], {q, 1, 12}];

Table[Flatten[Table[Table[w[n, m, q], {m, 1, n}], {n, 1, 10}]], {q, 1, 12}]

CROSSREFS

Sequence in context: A156765 A015117 A287020 * A075377 A046792 A209330

Adjacent sequences:  A172372 A172373 A172374 * A172376 A172377 A172378

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Feb 01 2010

STATUS

approved

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Last modified February 23 21:20 EST 2020. Contains 332195 sequences. (Running on oeis4.)