A327417 -id:A327417 - cp's OEIS frontend

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

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

Offset: 0

Peter Luschny, Sep 14 2019

nonn

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).

@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)])

A327418 a(n) = A291452(2*n, n).

Original entry on oeis.org

1, 1, 8255, 2941884000, 11957867341948125, 294040106448733743008625, 30188472144950452369737153667500, 10143939867539251013312279527292897925000, 9389957475743686923255643914812959599614184703125, 21058194888200109612591474039339954750056969537259132421875

Offset: 0

Peter Luschny, Sep 14 2019

nonn

Cf. A007820 (m=1), A327416 (m=2), A327417 (m=3), this sequence (m=4).

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

# uses[P from A327416]
def A327418(n): return P(4, 2*n).list()[n]//factorial(n)
print([A327418(n) for n in range(10)])

cp's OEIS Frontend

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

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