login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A132818 The matrix product A127773 * A001263 of infinite lower triangular matrices. 3

%I

%S 1,3,3,6,18,6,10,60,60,10,15,150,300,150,15,21,315,1050,1050,315,21,

%T 28,588,2940,4900,2940,588,28,36,1008,7056,17640,17640,7056,1008,36,

%U 45,1620,15120,52920,79380,52920,15120,1620,45,55,2475,29700,138600,291060

%N The matrix product A127773 * A001263 of infinite lower triangular matrices.

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

%F 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

%F 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

%e First few rows of the triangle are:

%e 1;

%e 3, 3;

%e 6, 18, 6;

%e 10, 60, 60, 10;

%e 15, 150, 300, 150, 15;

%e 21, 315, 1050, 1050, 315, 21;

%e ...

%p A132818 := proc(n,k)

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

%p end proc: # _R. J. Mathar_, Jul 29 2015

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

%K nonn,tabl,easy

%O 1,2

%A _Gary W. Adamson_, Sep 02 2007

%E Corrected by _R. J. Mathar_, Jul 29 2015

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 27 15:50 EST 2020. Contains 338683 sequences. (Running on oeis4.)