OFFSET
2,2
FORMULA
a(n) = A090438(n, 4), n>=2.
a(n) = (n-1)*(2*n-3)*(2*n)!/4! = binomial(2*(n-1), 2)*(2*n)!/4! = A000384(n-1)*(2*n)!/4!, n>=2.
E.g.f.: (6*hypergeom([1/2, 1], [], 4*x) - 4*hypergeom([1, 3/2], [], 4*x) + hypergeom([3/2, 2], [], 4*x) -3)/4! (cf. A090438).
From Amiram Eldar, Nov 03 2022: (Start)
Sum_{n>=2} 1/a(n) = -20 + 24*Gamma - 16*CoshIntegral(1) + 16*sinh(1) + 8*SinhIntegral(1).
Sum_{n>=2} (-1)^n/a(n) = 4 - 24*gamma + 16*cos(1) + 24*CosIntegral(1) - 16*sin(1) + 8*SinIntegral(1). (End)
MATHEMATICA
a[n_] := (n-1)*(2*n-3)*(2*n)!/4!; Array[a, 12, 2] (* Amiram Eldar, Nov 03 2022 *)
PROG
(PARI) a(n) = (n-1)*(2*n-3)*(2*n)!/4!; \\ Amiram Eldar, Nov 03 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jan 23 2004
STATUS
approved