A304944 a(0) = 0, a(1) = 1 and a(n) = 6*a(n-1)/(n-1) + 16*a(n-2) for n > 1.

0, 1, 6, 34, 164, 790, 3572, 16212, 71048, 312678, 1345220, 5809980, 24692600, 105305980, 443684360, 1875046120, 7848968208, 32944100998, 137210821092, 572842556332, 2376270786840, 9878362137364, 40842721771544, 169192718317336, 697620779210096

Offset

0,3

Comments

Let a(0) = 0, a(1) = 1 and a(n) = 2*m*a(n-1)/(n-1) + k^2*a(n-2) for n > 1, then the g.f. is x/(2*m) * d/dx ((1 + k*x)/(1 - k*x))^(m/k).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) = n*A304941(n)/6.

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

Mathematica

CoefficientList[Series[x/((1-4*x)^(7/4)*(1+4*x)^(1/4)), {x, 0, 40}], x] (* G. C. Greubel, Jun 07 2023 *)

Prog

(Magma) [n le 2 select n-1 else 2*(3*Self(n-1) + 8*(n-2)*Self(n-2))/(n-2): n in [1..40]]; // G. C. Greubel, Jun 07 2023
(SageMath)
@CachedFunction
def a(n): # b = A304944
    if n<2: return n
    else: return 2*(3*a(n-1) + 8*(n-1)*a(n-2))//(n-1)
[a(n) for n in range(41)] # G. C. Greubel, Jun 07 2023

Crossrefs

Cf. A304933, A304941.

Sequence in context: A086934 A009469 A222190 * A344717 A266359 A198765

Adjacent sequences: A304941 A304942 A304943 * A304945 A304946 A304947

Keyword

nonn

Author

Seiichi Manyama, May 22 2018

Status

approved