cp's OEIS Frontend

A132818 The matrix product A127773 * A001263 of infinite lower triangular matrices.

%I A132818 #15 Jul 29 2015 14:25:46
%S A132818 1,3,3,6,18,6,10,60,60,10,15,150,300,150,15,21,315,1050,1050,315,21,
%T A132818 28,588,2940,4900,2940,588,28,36,1008,7056,17640,17640,7056,1008,36,
%U A132818 45,1620,15120,52920,79380,52920,15120,1620,45,55,2475,29700,138600,291060
%N A132818 The matrix product A127773 * A001263 of infinite lower triangular matrices.
%F A132818 T(n,k) = A000217(n) * A001263(n,k).
%F A132818 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 A132818 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 A132818 First few rows of the triangle are:
%e A132818 1;
%e A132818 3, 3;
%e A132818 6, 18, 6;
%e A132818 10, 60, 60, 10;
%e A132818 15, 150, 300, 150, 15;
%e A132818 21, 315, 1050, 1050, 315, 21;
%e A132818 ...
%p A132818 A132818 := proc(n,k)
%p A132818     (n+1-k)*binomial(n+1,k)*binomial(n,k-1)/2 ;
%p A132818 end proc: # _R. J. Mathar_, Jul 29 2015
%Y A132818 Cf. A127773, A001263, A002457 (row sums), A006472. A002695, A008459.
%K A132818 nonn,tabl,easy
%O A132818 1,2
%A A132818 _Gary W. Adamson_, Sep 02 2007
%E A132818 Corrected by _R. J. Mathar_, Jul 29 2015