A368584 Table read by rows: T(n, k) = A124320(n + 1, k) * A048993(n, k).
1, 0, 2, 0, 3, 12, 0, 4, 60, 120, 0, 5, 210, 1260, 1680, 0, 6, 630, 8400, 30240, 30240, 0, 7, 1736, 45360, 327600, 831600, 665280, 0, 8, 4536, 216720, 2772000, 13305600, 25945920, 17297280, 0, 9, 11430, 956340, 20207880, 162162000, 575134560, 908107200, 518918400
Offset: 0
Examples
Triangle starts: [0] [1] [1] [0, 2] [2] [0, 3, 12] [3] [0, 4, 60, 120] [4] [0, 5, 210, 1260, 1680] [5] [0, 6, 630, 8400, 30240, 30240] [6] [0, 7, 1736, 45360, 327600, 831600, 665280] [7] [0, 8, 4536, 216720, 2772000, 13305600, 25945920, 17297280]
Links
- Elena L. Wang and Guoce Xin, On Ward Numbers and Increasing Schröder Trees, arXiv:2507.15654 [math.CO], 2025. See p. 12.
Crossrefs
Programs
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SageMath
def Trow(n): return [rising_factorial(n+1, k)*stirling_number2(n, k) for k in range(n+1)] for n in range(7): print(Trow(n))