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 A132121 Triangle read by rows: T(n,k)=n*(n+1)*((3*k+2)*n+1)/6, 0<=k<=n. 8
 0, 1, 2, 5, 11, 17, 14, 32, 50, 68, 30, 70, 110, 150, 190, 55, 130, 205, 280, 355, 430, 91, 217, 343, 469, 595, 721, 847, 140, 336, 532, 728, 924, 1120, 1316, 1512, 204, 492, 780, 1068, 1356, 1644, 1932, 2220, 2508, 285, 690, 1095, 1500, 1905, 2310, 2715, 3120 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row sums give A132122; central terms give A132123 T(n,0) = A000330(n); T(n,1) = A033994(n) for n>0; T(n,2) = A132124(n) for n>1; T(n,3) = A132112(n) for n>2; T(n,4) = A050409(n) for n>3. LINKS FORMULA G.f.: Sum_{n>=0} Sum_{k>=0} T(n,k)*x^n*y^k = x*(x*y+1+x)/((1-x)^4*(1-y)^2). - R. J. Mathar, Jul 28 2016. Note that this generates a full array, not just the triangular subspace. EXAMPLE 0; 1, 2; 5, 11, 17; 14, 32, 50, 68; 30, 70, 110, 150, 190; 55, 130, 205, 280, 355, 430; 91, 217, 343, 469, 595, 721, 847; 140, 336, 532, 728, 924, 1120, 1316, 1512; 204, 492, 780, 1068, 1356, 1644, 1932, 2220, 2508; MAPLE A132121 := proc(n, k)     n*(n+1)*((3*k+2)*n+1)/6 ; end proc: seq(seq(A132121(n, k), k=0..n), n=0..13) ; # R. J. Mathar, Feb 19 2020 CROSSREFS Sequence in context: A281023 A118660 A009770 * A070957 A166744 A080165 Adjacent sequences:  A132118 A132119 A132120 * A132122 A132123 A132124 KEYWORD nonn,tabl AUTHOR Reinhard Zumkeller, Aug 12 2007 STATUS approved

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Last modified September 18 06:40 EDT 2020. Contains 337166 sequences. (Running on oeis4.)