A373426 - OEIS

%I #6 Jun 13 2024 08:31:37

%S 1,0,1,0,2,1,0,6,12,7,1,0,24,108,144,73,15,1,0,120,1080,2640,2660,

%T 1221,267,27,1,0,720,11880,48720,82980,67350,28321,6344,751,44,1,0,

%U 5040,146160,955080,2529240,3262350,2245782,870283,195074,25267,1831,68,1

%N 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.

%H Peter Luschny, <a href="/A373426/a373426.png">Illustrating the polynomials</a>.

%e Tracing the computation:

%e   0: [1] *       [1] =                [1]

%e   1: [1] *       [0,  1] =            [0,  1]

%e   2: [1] *       [0,  2,  1] =        [0,  2,   1]

%e   3: [1, 1] *    [0,  6,  6,  1] =    [0,  6,  12,   7,  1]

%e   4: [1, 3, 1] * [0, 24, 36, 12, 1] = [0, 24, 108, 144, 73, 15, 1]

%p # Using function EZP from A373432.

%p EZP((n, k) -> ifelse(n=k, 1, binomial(n-1, k-1)*n!/k!), 7);

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

%K nonn,tabf

%O 0,5

%A _Peter Luschny_, Jun 07 2024