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 A158824 Triangle T(n,k) = A000292(n) if k = 1 otherwise (k-1)*(n-k+1)*(n-k+2)/2, read by rows. 3
 1, 4, 1, 10, 3, 2, 20, 6, 6, 3, 35, 10, 12, 9, 4, 56, 15, 20, 18, 12, 5, 84, 21, 30, 30, 24, 15, 6, 120, 28, 42, 45, 40, 30, 18, 7, 165, 36, 56, 63, 60, 50, 36, 21, 8, 220, 45, 72, 84, 84, 75, 60, 42, 24, 9, 286, 55, 90, 108, 112, 105, 90, 70, 48, 27, 10, 364, 66, 110, 135, 144, 140, 126, 105, 80, 54, 30, 11 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The triangle can also be defined by multiplying the triangles A(n,k)=1 and A158823(n,k), that is, this here are the partial column sums of A158823. LINKS G. C. Greubel, Rows n = 1..50 of the triangle, flattened FORMULA T(n,k) = binomial(n+2,3) if k = 1 otherwise (k-1)*binomial(n-k+2, 2). Sum_{k=1..n} T(n, k) = binomial(n+3, 4) = A000332(n+3). - G. C. Greubel, Apr 01 2021 EXAMPLE First few rows of the triangle are: 1; 4, 1; 10, 3, 2; 20, 6, 6, 3; 35, 10, 12, 9, 4; 56, 15, 20, 18, 12, 5; 84, 21, 30, 30, 24, 15, 6; 120, 28, 42, 45, 40, 30, 18, 7; 165, 36, 56, 63, 60, 50, 36, 21, 8; 220, 45, 72, 84, 84, 75, 60, 42, 24, 9; 286, 55, 90, 108, 112, 105, 90, 70, 48, 27, 10; 364, 66, 110, 135, 144, 140, 126, 105, 80, 54, 30, 11; 455, 78, 132, 165, 180, 180, 168, 147, 120, 90, 60, 33, 12; ... MATHEMATICA T[n_, k_]:= If[k==1, Binomial[n+2, 3], (k-1)*Binomial[n-k+2, 2]]; Table[T[n, k], {n, 12}, {k, n}]//Flatten (* G. C. Greubel, Apr 01 2021 *) PROG (Magma) A158824:= func< n, k | k eq 1 select Binomial(n+2, 3) else (k-1)*Binomial(n-k+2, 2) >; [A158824(n, k): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 01 2021 (Sage) def A158824(n, k): return binomial(n+2, 3) if k==1 else (k-1)*binomial(n-k+2, 2) flatten([[A158824(n, k) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Apr 01 2021 CROSSREFS Cf. A062707, A104633, A158823. Row sums: A000332. Sequence in context: A006370 A262370 A108759 * A348074 A334161 A039806 Adjacent sequences: A158821 A158822 A158823 * A158825 A158826 A158827 KEYWORD nonn,tabl,easy AUTHOR Gary W. Adamson & Roger L. Bagula, Mar 28 2009 STATUS approved

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Last modified April 25 04:42 EDT 2024. Contains 371964 sequences. (Running on oeis4.)