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

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

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

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

Programs

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

Mathematica

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

PARI

my(x='x+O('x^66)); Vec( 1/(2+x)+3/((2+x)*sqrt(1-4*x))-1 ) \\ Joerg Arndt, May 04 2013

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

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)