A373427 Triangle read by rows: Coefficients of the polynomials SC(n, x) * EZ(n, x), where SC denote the Stirling cycle polynomials and EZ the Eulerian zig-zag polynomials A205497.
1, 0, 1, 0, 1, 1, 0, 2, 5, 4, 1, 0, 6, 29, 45, 30, 9, 1, 0, 24, 218, 553, 629, 366, 112, 17, 1, 0, 120, 1954, 7781, 13409, 12136, 6270, 1894, 326, 29, 1, 0, 720, 20484, 125968, 313715, 407297, 308286, 143725, 42124, 7683, 830, 47, 1
Offset: 0
Examples
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, 5, 4, 1] 4: [1, 3, 1] * [0, 6, 11, 6, 1] = [0, 6, 29, 45, 30, 9, 1] 5: [1, 7, 7, 1] * [0, 24, 50, 35, 10, 1] = [0, 24, 218, 553, 629, 366, 112,17,1]
Links
- Peter Luschny, Illustrating the polynomials.
Crossrefs
Programs
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Maple
EZP((n, k) -> abs(Stirling1(n, k)), 7); # Using function EZP from A373432.