|
| |
|
|
A141223
|
|
Expansion of 1/(sqrt(1-4*x)*(1-3*x*c(x))), where c(x) is the g.f. of A000108.
|
|
1
| |
|
|
1, 5, 24, 113, 526, 2430, 11166, 51105, 233190, 1061510, 4822984, 21879786, 99135076, 448707992, 2029215114, 9170247393, 41416383366, 186957126702, 843575853984, 3804927658878, 17156636097156, 77339426905812
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Binomial transform of A126932. Hankel transform is (-1)^n.
Row sums of the Riordan matrix (1/(1-4*x),(1-sqrt(1-4*x))/(2*sqrt(1-4*x)) (A188481). [Emanuele Munarini, Apr 1 2001]
|
|
|
FORMULA
| a(n)=sum{k=0..n, C(2n-k,n-k)*3^k}
Contribution from Emanuele Munarini, Apr 1 2011. (Start)
a(n) = [x^n] 1/((1+x)^(n+1)*(1-3x)).
a(n) = 3^(2n+1)/2^(n+2) + (1/4)*sum(binomial(2k,k)*(9/2)^(n-k),k=0..n)
Recurrence: 2*(n+2)*a(n+2) - (17*n+30)*a(n+1) + 18*(2*n+3)*a(n) = 0
G.f.: (3-12*x+sqrt(1-4*x))/(4-34*x+72*x^2) (End)
|
|
|
MATHEMATICA
| CoefficientList[Series[(3-12x+Sqrt[1-4x])/(4-34x+72x^2), {x, 0, 100}], x] [Emanuele Munarini, Apr 1 2011]
|
|
|
PROG
| (Maxima) makelist(sum(binomial(n+k, k)*3^(n-k), k, 0, n), n, 0, 12); [Emanuele Munarini, Apr 1 2011]
|
|
|
CROSSREFS
| Sequence in context: A171310 A081104 A079028 * A140766 A026388 A057969
Adjacent sequences: A141220 A141221 A141222 * A141224 A141225 A141226
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jun 14 2008
|
| |
|
|
