A273019 a(n) = hypergeom([-2*n-1, 1/2], [2], 4) + (2*n+1)*hypergeom([-n+1/2, -n], [2], 4).

1, 5, 39, 321, 2675, 22483, 190345, 1621413, 13882947, 119385663, 1030434069, 8921880135, 77459553549, 674100041501, 5878674505303, 51361306358401, 449476337521875, 3939287035681807, 34570459724919253, 303749080936528883, 2671775251987354377, 23524418982229636185

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

Conjecture: +(241*n+56) *(2*n+1) *(n+1)*a(n) +(482*n^3-25561*n^2+13831*n-56) *a(n-1) +(-48682*n^3+225897*n^2-300131*n+125310) *a(n-2) +9*(n-2) *(2651*n-3183) *(2*n-3) *a(n-3)=0. - R. J. Mathar, May 16 2016

Recurrence (of order 2): (n+1)*(2*n + 1)*(12*n^2 - 19*n + 9)*a(n) = (240*n^4 - 140*n^3 - 42*n^2 - 7*n + 9)*a(n-1) - 9*(n-1)*(2*n - 1)*(12*n^2 + 5*n + 2)*a(n-2). - Vaclav Kotesovec, Jul 05 2018

a(n) ~ 3^(2*n + 3/2) / (2^(3/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 05 2018

Maple

a := n -> hypergeom([-2*n-1, 1/2], [2], 4) + (2*n+1)*hypergeom([-n+1/2, -n], [2], 4): seq(simplify(a(n)), n=0..22);

Mathematica

Table[HypergeometricPFQ[{-2*n-1, 1/2}, {2}, 4] + (2*n+1)*HypergeometricPFQ[ {-n+1/2, -n}, {2}, 4], {n, 0, 20}] (* Vaclav Kotesovec, Jul 05 2018 *)

Prog

def A():
    a, b, c, d, n = 0, 1, 1, -1, 1
    while True:
        if n%2: yield d + b*(1-(-1)^n)
        n += 1
        a, b = b, (3*(n-1)*n*a+(2*n-1)*n*b)//((n+1)*(n-1))
        c, d = d, (3*(n-1)*c-(2*n-1)*d)//n
A273019 = A()
print([A273019.next() for _ in range(22)])

Crossrefs

Bisection of A273020.

Cf. A082758.

Sequence in context: A135849 A105426 A356622 * A244039 A328554 A213233

Adjacent sequences: A273016 A273017 A273018 * A273020 A273021 A273022

Keyword

nonn

Author

Peter Luschny, May 13 2016

Status

approved