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 A262226 Eulerian numbers of type D, the primary type. 1
 1, 1, 0, 1, 2, 1, 1, 10, 13, 0, 1, 36, 118, 36, 1, 1, 116, 846, 836, 121, 0, 1, 358, 5279, 11764, 5279, 358, 1, 1, 1086, 30339, 129844, 129879, 30318, 1093, 0, 1, 3272, 165820, 1242616, 2337542, 1242616, 165820, 3272, 1, 1, 9832, 878188, 10853944, 34706710, 34706584, 10854028, 878152, 9841, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Named D(n, k) (the primary type D triangle) in Borowiec link. LINKS Anna Borowiec, Wojciech Mlotkowski, New Eulerian numbers of type D, arXiv:1509.03758 [math.CO], 2015. Katarzyna Kril, Wojciech Mlotkowski, Permutations of Type B with Fixed Number of Descents and Minus Signs, Volume 26(1) of The Electronic Journal of Combinatorics, 2019. FORMULA T(n, k) = (A060187(n+1, k+1) + (-1)^k*binomial(n, k))/2. EXAMPLE Triangle begins:   1;   1,   0;   1,   2,    1;   1,  10,   13,     0;   1,  36,  118,    36,    1;   1, 116,  846,   836,  121,   0;   1, 358, 5279, 11764, 5279, 358, 1;   ... MATHEMATICA T[n_, k_] := (Sum[(-1)^(k-i+1)(2i-1)^n Binomial[n+1, k-i+1], {i, 1, k+1}] + (-1)^k Binomial[n, k])/2; Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Sep 24 2018 *) PROG (PARI) B(n, k) = if( n

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Last modified June 25 09:48 EDT 2019. Contains 324347 sequences. (Running on oeis4.)