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

Author

Peter Luschny, Jan 10 2024

Keywords

• nonn
• tabl

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

Cf. A124320 (rising factorial), A048993(Stirling2), A053492 (row sums), A213236 (alternating row sums), A001813 (main diagonal), A368583.

Programs

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))