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 A173567 Triangle T(n, k) = (f(k, n-k+1) + f(n-k+1, k))/2 where f(n, k) = (1/2)*Sum_{j=1..2*n} k^j, read by rows. 1
 2, 5, 5, 9, 30, 9, 14, 123, 123, 14, 20, 425, 1092, 425, 20, 27, 1413, 7650, 7650, 1413, 27, 35, 4872, 54051, 87380, 54051, 4872, 35, 44, 17783, 426573, 943190, 943190, 426573, 17783, 44, 54, 67875, 3655854, 12192579, 12207030, 12192579, 3655854, 67875, 54 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Rows n = 1..50 of the triangle, flattened FORMULA T(n, k) = (f(k, n-k+1) + f(n-k+1, k))/2 where f(n, k) = (1/2)*Sum_{j=1..2*n} k^j. T(n, k) = (f(k, n-k+1) + f(n-k+1, k))/2 where f(n, k) = k*(1 - k^(2*n))/(1-k) with f(n, 1) = 2*n. - G. C. Greubel, Apr 25 2021 EXAMPLE Triangle begins as:    2;    5,     5;    9,    30,       9;   14,   123,     123,       14;   20,   425,    1092,      425,       20;   27,  1413,    7650,     7650,     1413,       27;   35,  4872,   54051,    87380,    54051,     4872,      35;   44, 17783,  426573,   943190,   943190,   426573,   17783,    44;   54, 67875, 3655854, 12192579, 12207030, 12192579, 3655854, 67875, 54; MATHEMATICA f[n_, k_]:= If[k==1, 2*n, k*(1-k^(2*n))/(1-k)]; T[n_, k_]:= (f[k, n-k+1] + f[n-k+1, k])/2; Table[T[n, k], {n, 10}, {k, n}]//Flatten (* modified by G. C. Greubel, Apr 25 2021 *) PROG (Sage) def f(n, k): return 2*n if k==1 else k*(1-k^(2*n))/(1-k) def T(n, k): return (f(k, n-k+1) + f(n-k+1, k))/2 flatten([[T(n, k) for k in (1..n)] for n in (1..10)]) # G. C. Greubel, Apr 25 2021 CROSSREFS Sequence in context: A050175 A243333 A059797 * A288726 A265129 A212624 Adjacent sequences:  A173564 A173565 A173566 * A173568 A173569 A173570 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Feb 22 2010 EXTENSIONS Edited by G. C. Greubel, Apr 25 2021 STATUS approved

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Last modified May 12 02:23 EDT 2021. Contains 343808 sequences. (Running on oeis4.)