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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.
2
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
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).
Sequence in context: A269942 A094645 A105793 * A158566 A128410 A059782
KEYWORD
sign,tabf
AUTHOR
Peter Luschny, Jun 07 2024
STATUS
approved