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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.
2
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
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
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, Jun 07 2024
STATUS
approved