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 A174098 Symmetrical triangle T(n, m) = floor(Eulerian(n+1, m)/2), read by rows. 1
 2, 5, 5, 13, 33, 13, 28, 151, 151, 28, 60, 595, 1208, 595, 60, 123, 2146, 7809, 7809, 2146, 123, 251, 7304, 44117, 78095, 44117, 7304, 251, 506, 23920, 227596, 655177, 655177, 227596, 23920, 506, 1018, 76318, 1101744, 4869057, 7862124, 4869057, 1101744, 76318, 1018 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Row sums are: {2, 10, 59, 358, 2518, 20156, 181439, 1814398, 19958398, 239500796, 3113510398, 43589145596, 653837183996, ...}. LINKS G. C. Greubel, Rows n = 2..100 of triangle, flattened FORMULA T(n, m) = floor(Eulerian(n+1, m)/2), where Eulerian(n,k) = A008292(n,k). EXAMPLE Triangle begins as:     2;     5,     5;    13,    33,     13;    28,   151,    151,     28;    60,   595,   1208,    595,     60;   123,  2146,   7809,   7809,   2146,    123;   251,  7304,  44117,  78095,  44117,   7304,   251;   506, 23920, 227596, 655177, 655177, 227596, 23920, 506; MATHEMATICA Eulerian[n_, k_]:= Sum[(-1)^j*Binomial[n+1, j]*(k-j+1)^n, {j, 0, k+1}]; Table[Floor[Eulerian[n+1, m]/2], {n, 2, 12}, {m, 1, n-1}]//Flatten (* G. C. Greubel, Apr 25 2019 *) PROG (PARI) {T(n, k) = (sum(j=0, k+1, (-1)^j*binomial(n+2, j)*(k-j+1)^(n+1)))\2}; for(n=2, 12, for(k=1, n-1, print1(T(n, k), ", "))) \\ G. C. Greubel, Apr 25 2019 (MAGMA) [[Floor((&+[(-1)^j*Binomial(n+2, j)*(k-j+1)^(n+1): j in [0..k+1]] )/2): k in [1..n-1]]: n in [2..12]]; // G. C. Greubel, Apr 25 2019 (Sage) [[floor(sum((-1)^j*binomial(n+2, j)*(k-j+1)^(n+1) for j in (0..k+1))/2) for k in (1..n-1)] for n in (2..12)] # G. C. Greubel, Apr 25 2019 CROSSREFS Cf. A008292, A166454. Sequence in context: A154692 A309161 A144293 * A183419 A305314 A154694 Adjacent sequences:  A174095 A174096 A174097 * A174099 A174100 A174101 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Mar 07 2010 EXTENSIONS Edited by G. C. Greubel, Apr 25 2019 STATUS approved

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Last modified May 12 23:09 EDT 2021. Contains 343829 sequences. (Running on oeis4.)