A327416 a(n) = A156289(2*n, n).

1, 1, 63, 21120, 20585565, 44025570225, 175418438510700, 1169944052730453000, 12110024900113702687125, 183906442861089163922581875, 3923248989041777334572795737575, 113570018319217734510803494872644700, 4337118170117525113961286942555563803500

Offset: 0

Author

Peter Luschny, Sep 14 2019

Keywords

• nonn

Crossrefs

Cf. A007820 (m=1), this sequence (m=2), A327417 (m=3), A327418 (m=4).

Associated triangles: A048993 (m=1), A156289 (m=2), A291451 (m=3), A291452 (m=4).

Programs

SageMath

@cached_function
def P(m, n):
    x = polygen(ZZ)
    if n == 0: return x^0
    return expand(sum(binomial(m*n, m*k)*P(m, n-k)*x for k in (1..n)))
def A327416(n): return P(2, 2*n).list()[n]//factorial(n)
print([A327416(n) for n in range(13)])