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A132818 The matrix product A127773 * A001263 of infinite lower triangular matrices. 3
1, 3, 3, 6, 18, 6, 10, 60, 60, 10, 15, 150, 300, 150, 15, 21, 315, 1050, 1050, 315, 21, 28, 588, 2940, 4900, 2940, 588, 28, 36, 1008, 7056, 17640, 17640, 7056, 1008, 36, 45, 1620, 15120, 52920, 79380, 52920, 15120, 1620, 45, 55, 2475, 29700, 138600, 291060 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..50.

FORMULA

T(n,k) = A000217(n) * A001263(n,k).

Let a(n) = A006472(n), the 'triangular' factorial numbers. Then a(n)/(a(k)*a(n-k)) produces the present triangle (with a different offset). - Peter Bala, Dec 07 2011

T(n,k) = 1/2*(n+1-k)*C(n+1,k)*C(n,k-1), for n,k >= 1. O.g.f.: x*y/((1-x-x*y)^2 - 4*x^2*y)^(3/2) = x*y + x^2*(3*y + 3*y^2) + x^3*(6*y + 18*y^2 + 6*y^3) + .... Cf. A008459 with o.g.f.: x*y/((1-x-x*y)^2 - 4*x^2*y)^(1/2). Sum {k = 1..n-1} T(n,k)*2^(n-k) = A002695(n). - Peter Bala, Apr 10 2012

EXAMPLE

First few rows of the triangle are:

1;

3, 3;

6, 18, 6;

10, 60, 60, 10;

15, 150, 300, 150, 15;

21, 315, 1050, 1050, 315, 21;

...

MAPLE

A132818 := proc(n, k)

    (n+1-k)*binomial(n+1, k)*binomial(n, k-1)/2 ;

end proc: # R. J. Mathar, Jul 29 2015

CROSSREFS

Cf. A127773, A001263, A002457 (row sums), A006472. A002695, A008459.

Sequence in context: A123104 A038076 A123286 * A134068 A025256 A052560

Adjacent sequences:  A132815 A132816 A132817 * A132819 A132820 A132821

KEYWORD

nonn,tabl,easy

AUTHOR

Gary W. Adamson, Sep 02 2007

EXTENSIONS

Corrected by R. J. Mathar, Jul 29 2015

STATUS

approved

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Last modified October 24 21:12 EDT 2020. Contains 338010 sequences. (Running on oeis4.)