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A173424 Triangle T(n,m) read by rows: (2*n - 2*m)!*(2*m)!/( 2^n*(n - m)!*m! ) 0
1, 1, 1, 3, 1, 3, 15, 3, 3, 15, 105, 15, 9, 15, 105, 945, 105, 45, 45, 105, 945, 10395, 945, 315, 225, 315, 945, 10395, 135135, 10395, 2835, 1575, 1575, 2835, 10395, 135135, 2027025, 135135, 31185, 14175, 11025, 14175, 31185, 135135, 2027025, 34459425 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are: 1, 2, 7, 36, 249, 2190, 23535, 299880, 4426065, 74294010, 1397669175, ..., apparently A034430.

LINKS

Table of n, a(n) for n=0..45.

FORMULA

T(n,m)= A006882(2*n-2*m-1)* A006882(2*m-1) = A001147(n-m)*A001147(m).

EXAMPLE

1;

1, 1;

3, 1, 3;

15, 3, 3, 15;

105, 15, 9, 15, 105;

945, 105, 45, 45, 105, 945;

10395, 945, 315, 225, 315, 945, 10395;

135135, 10395, 2835, 1575, 1575, 2835, 10395, 135135;

2027025, 135135, 31185, 14175, 11025, 14175, 31185, 135135, 2027025;

34459425, 2027025, 405405, 155925, 99225, 99225, 155925, 405405, 2027025, 34459425;

654729075, 34459425, 6081075, 2027025, 1091475, 893025, 1091475, 2027025, 6081075, 34459425, 654729075;

MATHEMATICA

t[n_, m_] = (2*n - 2*m)!*(2*m)!/(2^n*(n - m)!*m!);

Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A351372 A356411 A355793 * A143081 A179658 A112811

Adjacent sequences:  A173421 A173422 A173423 * A173425 A173426 A173427

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Feb 18 2010

EXTENSIONS

Formula added by the Assoc. Editors of the OEIS, Feb 24 2010

STATUS

approved

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Last modified August 18 02:34 EDT 2022. Contains 356204 sequences. (Running on oeis4.)