This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A262227 Eulerian numbers of type D, the complementary type. 1
 0, 0, 1, 0, 4, 0, 0, 13, 10, 1, 0, 40, 112, 40, 0, 0, 121, 836, 846, 116, 1, 0, 364, 5264, 11784, 5264, 364, 0, 0, 1093, 30318, 129879, 129844, 30339, 1086, 1, 0, 3280, 165792, 1242672, 2337472, 1242672, 165792, 3280, 0, 0, 9841, 878152, 10854028, 34706584, 34706710, 10853944, 878188, 9832, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Named D~(n, k) (the complementary type D triangle) in the 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:   0;   0,   1;   0,   4,    0;   0,  13,   10,     1;   0,  40,  112,    40,    0;   0, 121,  836,   846,  116,   1;   0, 364, 5264, 11784, 5264, 364, 0;   ... MATHEMATICA T[n_, k_] := (Sum[(-1)^(k - i + 1)*(2*i - 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, Feb 19 2019 *) PROG (PARI) B(n, k) = if( n

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 15 21:17 EDT 2019. Contains 328038 sequences. (Running on oeis4.)