# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a135065 Showing 1-1 of 1 %I A135065 #34 Jul 11 2023 12:04:17 %S A135065 1,4,4,9,18,9,16,48,48,16,25,100,150,100,25,36,180,360,360,180,36,49, %T A135065 294,735,980,735,294,49,64,448,1344,2240,2240,1344,448,64,81,648,2268, %U A135065 4536,5670,4536,2268,648,81,100,900,3600,8400,12600,12600,8400,3600 %N A135065 A127733 * A007318 as infinite lower triangular matrices. %C A135065 A135065 * [1/1, 1/2, 1/3, ...] = A066524: (1, 6, 21, 60, 155, ...). %C A135065 Triangle T(n,k), 0 <= k <= n, read by rows, given by (4, -7/4, 17/28, -32/119, 7/17, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (4, -7/4, 17/28, -32/119, 7/17, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - _Philippe Deléham_, Oct 27 2011 %H A135065 G. C. Greubel, Table of n, a(n) for the first 50 rows %H A135065 Mircea Merca, A Special Case of the Generalized Girard-Waring Formula, J. Integer Sequences, Vol. 15 (2012), Article 12.5.7. %F A135065 T(n,k) = binomial(n,k)*(n+1)^2 = A007318(n,k)*A000290(n+1). - _Philippe Deléham_, Oct 27 2011 %F A135065 T(n-1,k-1) = Sum_{i=-k..k} (-1)^i*(k^2-i^2)*binomial(n,k+i)*binomial(n,k-i). - _Mircea Merca_, Apr 05 2012 %F A135065 G.f.: (-1 - x - x*y)/(x + x*y - 1)^3. - _R. J. Mathar_, Aug 12 2015 %e A135065 First few rows of the triangle: %e A135065 1; %e A135065 4, 4; %e A135065 9, 18, 9; %e A135065 16, 48, 48, 16; %e A135065 25, 100, 150, 100, 25; %e A135065 36, 180, 360, 360, 180, 36; %e A135065 49, 294, 735, 980, 735, 294, 49; %p A135065 with(combstruct):for n from 0 to 11 do seq(n*m*count(Combination(n), size=m), m = 1 .. n) od; # _Zerinvary Lajos_, Apr 09 2008 %t A135065 Flatten[Table[Binomial[n,k](n+1)^2,{n,0,10},{k,0,n}]] (* _Harvey P. Dale_, Jul 12 2013 *) %Y A135065 Cf. A000290, A127733, A066524, A014477 (row sums), A084938. %K A135065 nonn,tabl,easy %O A135065 0,2 %A A135065 _Gary W. Adamson_, Nov 16 2007 %E A135065 Corrected by _Zerinvary Lajos_, Apr 09 2008 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE