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A142469 The nonzero difference between the Pascal {1,8,1} level triangle sequence and the {1,8,1} Catalan generalized triangle: t0(n,m)=Binomial[n, m]*Product[k!*(n + k)!/((m + k)!*(n - m + k)!), {k, 1, 7}]. A(n,k)=(3*n - 3*k + 1)A(n - 1, k - 1) + (3*k - 2)A(n - 1, k); t(n,m)=A(n,m)-t0(n,m). The first three levels and the external columns are zero and extracted. 0
3, 3, 46, 6, 46, 347, 532, 532, 347, 1932, 14505, 740, 14505, 1932, 9199, 203925, 152405, 152405, 203925, 9199, 40250, 2087884, 6882086, -86372, 6882086, 2087884, 40250, 168318, 17968725, 152844537, 78623775, 78623775, 152844537, 17968725, 168318 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row sums are:

{6, 98, 1758, 33614, 731058, 17934068, 499210710}.

LINKS

Table of n, a(n) for n=1..35.

FORMULA

t0(n,m)=Binomial[n, m]*Product[k!*(n + k)!/((m + k)!*(n - m + k)!), {k, 1, 7}]. A(n,k)=(3*n - 3*k + 1)A(n - 1, k - 1) + (3*k - 2)A(n - 1, k); t(n,m)=A(n,m)-t0(n,m).

EXAMPLE

{3, 3},

{46, 6, 46},

{347, 532, 532, 347},

{1932, 14505, 740, 14505, 1932},

{9199, 203925, 152405, 152405, 203925, 9199},

{40250, 2087884, 6882086, -86372, 6882086, 2087884, 40250},

{168318, 17968725, 152844537, 78623775, 78623775, 152844537, 17968725, 168318}

MATHEMATICA

f[0, 0] = 1; f[n_, m_] := f[n, m] = Binomial[n, m]*Product[k!*(n + k)!/((m + k)!*(n - m + k)!), {k, 1, 6}]; A[n_, 1] := 1 A[n_, n_] := 1 A[n_, k_] := (3*n - 3*k + 1)A[n - 1, k - 1] + (3*k - 2)A[n - 1, k]; a = Table[If[f[n - 1, k - 1] - A[n, k] == 0, {}, -f[n - 1, k - 1] + A[n, k]], {n, 10}, {k, n}]; c = Delete[Union[Table[Flatten[a[[n]]], {n, 1, 10}]], 1]; Flatten[a]

CROSSREFS

Sequence in context: A290366 A083391 A165636 * A009809 A265717 A292753

Adjacent sequences:  A142466 A142467 A142468 * A142470 A142471 A142472

KEYWORD

sign,uned

AUTHOR

Roger L. Bagula and Gary W. Adamson, Sep 20 2008

STATUS

approved

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Last modified August 8 19:29 EDT 2020. Contains 336298 sequences. (Running on oeis4.)