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A171822 Triangular sequence:t(n,k)=A085478[n,k]*A054142[n,k]=Binomial[2*n - k, k]*Binomial[n + k, 2*k] 0
1, 1, 1, 1, 9, 1, 1, 30, 30, 1, 1, 70, 225, 70, 1, 1, 135, 980, 980, 135, 1, 1, 231, 3150, 7056, 3150, 231, 1, 1, 364, 8316, 34650, 34650, 8316, 364, 1, 1, 540, 19110, 132132, 245025, 132132, 19110, 540, 1, 1, 765, 39600, 420420, 1288287, 1288287, 420420 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 11, 62, 367, 2232, 13820, 86662, 548591, 3498146, 22436251,...}.

A085478 is the reverse order of A054142 so that together they make a symmetrical triangle.

LINKS

Table of n, a(n) for n=0..51.

FORMULA

t(n,k)=Binomial[2*n - k, k]*Binomial[n + k, 2*k]

EXAMPLE

{1},

{1, 1},

{1, 9, 1},

{1, 30, 30, 1},

{1, 70, 225, 70, 1},

{1, 135, 980, 980, 135, 1},

{1, 231, 3150, 7056, 3150, 231, 1},

{1, 364, 8316, 34650, 34650, 8316, 364, 1},

{1, 540, 19110, 132132, 245025, 132132, 19110, 540, 1},

{1, 765, 39600, 420420, 1288287, 1288287, 420420, 39600, 765, 1},

{1, 1045, 75735, 1166880, 5465460, 9018009, 5465460, 1166880, 75735, 1045, 1}

MATHEMATICA

T[n_, k_] = Binomial[2*n - k, k]*Binomial[n + k, 2*k]

Table[Table[T[n, k], {k, 0, n}], {n, 0, 10}]

Flatten[%]

CROSSREFS

Cf. A085478, A054142

Sequence in context: A144404 A014761 A073702 * A176490 A174158 A181144

Adjacent sequences:  A171819 A171820 A171821 * A171823 A171824 A171825

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Dec 19 2009

STATUS

approved

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Last modified June 24 17:50 EDT 2019. Contains 324330 sequences. (Running on oeis4.)