A209358 G.f.: (1-4*x)^(-1/4) * (1-8*x)^(-1/8).

1, 2, 8, 40, 228, 1416, 9312, 63648, 446760, 3195728, 23179840, 169929280, 1256234720, 9350462400, 69993150720, 526455847680, 3976132184160, 30138433333440, 229168000121600, 1747455531216640, 13358199405416320, 102345801274115840, 785740341422453760

Offset

0,2

Links

Iain Fox, Table of n, a(n) for n = 0..1111 (first 201 terms from Vincenzo Librandi)

Formula

Equals the self-convolution square root of A209200, which equals the convolution of sequences A000984 and A004981.

Recurrence: n*a(n) = 2*(6*n-5)*a(n-1) - 4*(8*n-13)*a(n-2). - Vaclav Kotesovec, Oct 20 2012

a(n) ~ Gamma(7/8)*2^(1/4)*8^n*sin(Pi/8)/(n^(7/8)*Pi). - Vaclav Kotesovec, Oct 20 2012

Example

G.f.: A(x) = 1 + 2*x + 8*x^2 + 40*x^3 + 228*x^4 + 1416*x^5 + 9312*x^6 +...
such that the square of the g.f. A(x) equals the g.f. of A209200:
A(x)^2 = 1 + 4*x + 20*x^2 + 112*x^3 + 680*x^4 + 4384*x^5 + 29536*x^6 +...
Sequence A209200 equals the convolution of the sequences:
A000984 = [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620, ...],
A004981 = [1, 2, 10, 60, 390, 2652, 18564, 132600, 961350, ...].

Mathematica

CoefficientList[Series[(1-4*x)^(-1/4)*(1-8*x)^(-1/8), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 20 2012 *)

Prog

(PARI) {a(n)=polcoeff((1-4*x +x*O(x^n))^(-1/4)*(1-8*x +x*O(x^n))^(-1/8), n)}
for(n=0, 30, print1(a(n), ", "))
(Magma) I:=[2, 8]; [1] cat [n le 2 select I[n] else (2*(6*n-5)*Self(n-1) - 4*(8*n-13)*Self(n-2))/n: n in [1..30]]; // G. C. Greubel, Jan 03 2018

Crossrefs

Cf. A209200, A000984, A004981.

Sequence in context: A085485 A089603 A343146 * A116456 A341876 A305406

Adjacent sequences: A209355 A209356 A209357 * A209359 A209360 A209361

Keyword

nonn

Author

Paul D. Hanna, Mar 06 2012

Status

approved