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 A141689 Average of Eulerian numbers (A008292) and Pascal's triangle (A007318): t(n,m) = (A008292(n,m) + A007318(n,m))/2. 2
 1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 15, 36, 15, 1, 1, 31, 156, 156, 31, 1, 1, 63, 603, 1218, 603, 63, 1, 1, 127, 2157, 7827, 7827, 2157, 127, 1, 1, 255, 7318, 44145, 78130, 44145, 7318, 255, 1, 1, 511, 23938, 227638, 655240, 655240, 227638, 23938, 511, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row sums are: {1, 2, 5, 16, 68, 376, 2552, 20224, 181568, 1814656, ...}. If Pascal's triangle and the Eulerian numbers are both fundamental arrays, then there should be a combinatorial set "between" them. LINKS G. C. Greubel, Rows n=1..100 of triangle, flattened EXAMPLE {1}, {1, 1}, {1, 3, 1}, {1, 7, 7, 1}, {1, 15, 36, 15, 1}, {1, 31, 156, 156, 31, 1}, {1, 63, 603, 1218, 603, 63, 1}, {1, 127, 2157, 7827, 7827, 2157, 127, 1}, {1, 255, 7318, 44145, 78130, 44145, 7318, 255, 1}, {1, 511, 23938, 227638, 655240, 655240, 227638, 23938, 511, 1} MATHEMATICA Table[Table[(Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}] + Binomial[n - 1, k])/2, {k, 0, n - 1}], {n, 1, 10}]; Flatten[%] CROSSREFS Cf. A008292, A007318. Sequence in context: A046802 A184173 A022166 * A058669 A057004 A059328 Adjacent sequences:  A141686 A141687 A141688 * A141690 A141691 A141692 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Sep 09 2008 EXTENSIONS Edited by N. J. A. Sloane, Dec 13 2008 STATUS approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)