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A158117 Triangle sequence of general q-combinations: m=3; t(n,m)=t[n_, m_] = If[m == 0, n!, Product[((m + 1)*((m + 1) + 1)/2)^k, {k, 1, n}]]; b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])]. 0
1, 1, 1, 1, 10, 1, 1, 100, 100, 1, 1, 1000, 10000, 1000, 1, 1, 10000, 1000000, 1000000, 10000, 1, 1, 100000, 100000000, 1000000000, 100000000, 100000, 1, 1, 1000000, 10000000000, 1000000000000, 1000000000000, 10000000000, 1000000, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 12, 202, 12002, 2020002, 1200200002, 2020002000002, 12002000020000002,

202000200000200000002, 12002000020000002000000002,...}.

LINKS

Table of n, a(n) for n=0..36.

FORMULA

m=3;

t(n,m)=t[n_, m_] = If[m == 0, n!, Product[((m + 1)*((m + 1) + 1)/2)^k, {k, 1, n}]];

b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].

EXAMPLE

{1},

{1, 1},

{1, 10, 1},

{1, 100, 100, 1},

{1, 1000, 10000, 1000, 1},

{1, 10000, 1000000, 1000000, 10000, 1},

{1, 100000, 100000000, 1000000000, 100000000, 100000, 1},

{1, 1000000, 10000000000, 1000000000000, 1000000000000, 10000000000, 1000000, 1},

{1, 10000000, 1000000000000, 1000000000000000, 10000000000000000, 1000000000000000, 1000000000000, 10000000, 1},

{1, 100000000, 100000000000000, 1000000000000000000, 100000000000000000000, 100000000000000000000, 1000000000000000000, 100000000000000, 100000000, 1},

{1, 1000000000, 10000000000000000, 1000000000000000000000, 1000000000000000000000000, 10000000000000000000000000, 1000000000000000000000000, 1000000000000000000000, 10000000000000000, 1000000000, 1}

MATHEMATICA

t[n_, m_] = If[m == 0, n!, Product[((m + 1)*((m + 1) + 1)/2)^k, {k, 1, n}]];

b[n_, k_, m_] = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])];

Table[Flatten[Table[Table[b[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 15}]

CROSSREFS

A118180

Sequence in context: A160562 A176243 A022173 * A172378 A015124 A156767

Adjacent sequences:  A158114 A158115 A158116 * A158118 A158119 A158120

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 12 2009

STATUS

approved

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Last modified September 29 06:29 EDT 2020. Contains 337425 sequences. (Running on oeis4.)