OFFSET
0,2
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
Recurrence: n*a(n) = 4*(3*n-2)*a(n-1) - 8*(4*n-5)*a(n-2). - Vaclav Kotesovec, Oct 20 2012
a(n) ~ Gamma(3/4)*8^n/(Pi*n^(3/4)). - Vaclav Kotesovec, Oct 20 2012
EXAMPLE
G.f.: A(x) = 1 + 4*x + 60*x^2 + 1200*x^3 + 27300*x^4 + 668304*x^5 +...
This sequence equals the convolution of the sequences:
A000984 = [1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620, ...], and
A004981 = [1, 2, 10, 60, 390, 2652, 18564, 132600, 961350, ...].
Related sequences:
A^2: [1, 8, 56, 384, 2656, 18688, 133888, 974848, 7194112, ...],
A^4: [1, 16, 176, 1664, 14592, 122880, 1011712, 8224768, ...].
MATHEMATICA
CoefficientList[Series[(1-4*x)^(-1/2)*(1-8*x)^(-1/4), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 20 2012 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 06 2012
STATUS
approved