A373426 Triangle read by rows: Coefficients of the polynomials L(n, x) * EZ(n, x), where L denote the unsigned Lah polynomials and EZ the Eulerian zig-zag polynomials A205497.

1, 0, 1, 0, 2, 1, 0, 6, 12, 7, 1, 0, 24, 108, 144, 73, 15, 1, 0, 120, 1080, 2640, 2660, 1221, 267, 27, 1, 0, 720, 11880, 48720, 82980, 67350, 28321, 6344, 751, 44, 1, 0, 5040, 146160, 955080, 2529240, 3262350, 2245782, 870283, 195074, 25267, 1831, 68, 1

Offset

0,5

Links

Table of n, a(n) for n=0..50.

Peter Luschny, Illustrating the polynomials.

Example

Tracing the computation:
  0: [1] *       [1] =                [1]
  1: [1] *       [0,  1] =            [0,  1]
  2: [1] *       [0,  2,  1] =        [0,  2,   1]
  3: [1, 1] *    [0,  6,  6,  1] =    [0,  6,  12,   7,  1]
  4: [1, 3, 1] * [0, 24, 36, 12, 1] = [0, 24, 108, 144, 73, 15, 1]

Maple

# Using function EZP from A373432.
EZP((n, k) -> ifelse(n=k, 1, binomial(n-1, k-1)*n!/k!), 7);

Crossrefs

Cf. A271703 (Lah), A205497 (zig-zag Eulerian), A373425 (row sums).

Sequence in context: A187555 A358188 A117651 * A268728 A187196 A187197

Adjacent sequences: A373423 A373424 A373425 * A373427 A373428 A373429

Keyword

nonn,tabf

Author

Peter Luschny, Jun 07 2024

Status

approved