|
| |
|
|
A046748
|
|
Expansion of sqrt(1-4*x)/(1-5*x); row sums of triangle A046521.
|
|
5
| |
|
|
1, 3, 13, 61, 295, 1447, 7151, 35491, 176597, 880125, 4390901, 21920913, 109486993, 547018941, 2733608905, 13662695645, 68294088535, 341399727335, 1706739347095, 8532741458075, 42660172763995, 213287735579135
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| i)Homogeneous recursion: a(n) = (3*(3*n-2)/n)*a(n-1) - (10*(2*n-3)/n)*a(n-2), n >= 1, a(-1) := 0, a(0)=1. ii) Hypergeometric 2F1 form: a(n)=binomial(2*n,n)*hypergeom([ -n,1 ],[ 1/2 ],-1/4).
Hankel transform is A082761. [From Paul Barry (pbarry(AT)wit.ie), Apr 14 2010]
|
|
|
FORMULA
| a(n) = binomial(2*n, n)*sum(binomial(n, k)/binomial(2*k, k), k=0..n) = 5^n - 2*A046714(n-1), A046714(-1) := 0; a(n) = 5*a(n-1) - 2*A000108(n-1), A000108(n): Catalan; G.f. sqrt(1-4*x)/(1-5*x).
|
|
|
CROSSREFS
| A046521, A046714, A000108.
Sequence in context: A108143 A101368 A026704 * A200215 A074548 A141786
Adjacent sequences: A046745 A046746 A046747 * A046749 A046750 A046751
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
|
| |
|
|
