A264437 a(n) = Bernoulli(n, 1)*Pochhammer(n+1, n).
1, 1, 2, 0, -56, 0, 15840, 0, -17297280, 0, 50791104000, 0, -327856732600320, 0, 4080179409546240000, 0, -89192941330901151744000, 0, 3193957788339335451033600000, 0, -177450861021098776794591068160000, 0, 14644425624059165645548485417369600000, 0
Offset: 0
Keywords
Programs
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Maple
seq(pochhammer(n+1,n)*bernoulli(n,1),n=0..23); # For illustration: e1 := proc(n, k) combinat:-eulerian1(n, k) end: catalan := n -> binomial(2*n, n)/(n + 1): a := n -> catalan(n)*add(e1(n, k)*k!*(n - k)!*(-1)^k, k = 0..n): # Peter Luschny, Aug 13 2022
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Mathematica
a[n_] := BernoulliB[n, 1]*Pochhammer[n+1, n]; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Nov 13 2023 *) -
PARI
a(n) = subst(bernpol(n), 'x, 1) *(2*n)!/n!; \\ Michel Marcus, Nov 13 2023
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Sage
def A264437(n): return bernoulli_polynomial(1,n)*factorial(2*n)//factorial(n) [A264437(n) for n in range(24)]
Formula
a(n) = CatalanNumber(n)*Sum_{k=0..n} Eulerian1(n, k)*k!*(n - k)!*(-1)^k. # Peter Luschny, Aug 13 2022
Extensions
Name and data changed to comply with Bernoulli(n,1) by Peter Luschny, Aug 13 2022