A072477 a(n) = (2*n)!*binomial(2*n,n)/8.
18, 1800, 352800, 114307200, 55324684800, 37399486924800, 33659538232320000, 38910426196561920000, 56186655427835412480000, 99113260174701667614720000, 209723658529668728672747520000, 524309146324171821681868800000000, 1528885470681285032024329420800000000
Offset: 2
Links
- Michel Bousquet, Gilbert Labelle and Pierre Leroux, Enumeration of planar two-face maps, Discrete Mathematics, 222 (2000), 1-25.
Programs
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Mathematica
a[n_] := (2*n)!*Binomial[2*n, n]/8; Array[a, 12, 2] (* Amiram Eldar, Jun 18 2025 *)
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PARI
a(n) = (2*n)!*binomial(2*n, n)/8; \\ Amiram Eldar, Jun 18 2025
Formula
From Amiram Eldar, Jun 18 2025: (Start)
Sum_{n>=2} 1/a(n) = 2*Pi*L_0(1/2) - 2, where L is the modified Struve function.
Sum_{n>=2} (-1)^n/a(n) = 2 - 2*Pi*H_0(1/2), where H is the Struve function. (End)