A373429 Triangle read by rows: Coefficients of the polynomials S1(n, x) * EZ(n, x), where S1 denote the Stirling1 polynomials and EZ the Eulerian zig-zag polynomials A205497.

1, 0, 1, 0, -1, 1, 0, 2, -1, -2, 1, 0, -6, -7, 21, -6, -3, 1, 0, 24, 118, -147, -91, 126, -28, -3, 1, 0, -120, -1406, -109, 3749, -2084, -450, 514, -94, -1, 1, 0, 720, 16956, 34240, -72307, -15475, 56286, -21125, -674, 1635, -262, 5, 1

Offset

0,8

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, -1,  1] =              [0, -1,   1]
3: [1, 1] *       [0,  2,  -3,  1] =         [0,  2,  -1,   -2,   1]
4: [1, 3, 1] *    [0, -6,  11, -6,   1] =    [0, -6,  -7,   21,  -6,  -3,  1]
5: [1, 7, 7, 1] * [0, 24, -50, 35, -10, 1] = [0, 24, 118, -147, -91, 126,-28,-3,1]

Maple

EZP(Stirling1, 7);  # Using function EZP from A373432.

Crossrefs

Cf. A048994 (Stirling1), A205497 (zig-zag Eulerian), A320956 (row sums).

Cf. A373428, A373432.

Sequence in context: A269942 A094645 A105793 * A158566 A128410 A059782

Adjacent sequences: A373426 A373427 A373428 * A373430 A373431 A373432

Keyword

sign,tabf

Author

Peter Luschny, Jun 07 2024

Status

approved