A026638 a(n) = A026637(2*n, n).

1, 2, 8, 26, 92, 332, 1220, 4538, 17036, 64412, 244928, 935684, 3588392, 13806704, 53271548, 206040506, 798600332, 3101109164, 12062148368, 46986821516, 183276382472, 715748620424, 2798274135368, 10951009023716, 42895901012792, 168167959150232, 659793819847040

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

From Vaclav Kotesovec, Oct 21 2012: (Start)

G.f.: (3 - (x+1)*sqrt(1-4*x))/((x+2)*sqrt(1-4*x)).

Recurrence: 2*n*a(n) = (7*n-4)*a(n-1) + 2*(2*n-1)*a(n-2).

a(n) ~ 2^(2*n+2)/(3*sqrt(Pi*n)) (End)

Mathematica

CoefficientList[Series[1/(2+x)+3/((2+x)*Sqrt[1-4*x])-1, {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 21 2012 *)

Prog

(PARI) my(x='x+O('x^66)); Vec( 1/(2+x)+3/((2+x)*sqrt(1-4*x))-1 ) \\ Joerg Arndt, May 04 2013
(Magma) [1] cat [n le 2 select 2^(2*n-1) else ((7*n-4)*Self(n-1) + 2*(2*n-1)*Self(n-2))/(2*n): n in [1..40]]; // G. C. Greubel, Jul 01 2024
(SageMath)
@CachedFunction
def a(n): # a = A026638
    if n<3: return 2^(n*(n+1)/2)
    else: return ((7*n-4)*a(n-1) + 2*(2*n-1)*a(n-2))/(2*n)
[a(n) for n in range(41)] # G. C. Greubel, Jul 01 2024

Crossrefs

Cf. A026637, A026639, A026640, A026642, A026643, A026644, A026645.

Cf. A026646, A026647, A026966, A026967, A026968, A026969, A026970.

Sequence in context: A053956 A320802 A052543 * A307401 A067855 A301699

Adjacent sequences: A026635 A026636 A026637 * A026639 A026640 A026641

Keyword

nonn

Author

Clark Kimberling

Status

approved