|
| |
|
|
A084605
|
|
G.f.: 1/(1-2x-15x^2)^(1/2); also, a(n) is the central coefficient of (1+x+4x^2)^n.
|
|
5
| |
|
|
1, 1, 9, 25, 145, 561, 2841, 12489, 60705, 281185, 1353769, 6418809, 30917041, 148331665, 716698425, 3462260265, 16786700865, 81464917185, 396215601225, 1929237099225, 9408084660945, 45928695279345, 224476389327705
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Also number of paths from (0,0) to (n,0) using steps U=(1,1), H=(1,0) and D=(1,-1), the U (or D) steps come in four colors. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Mar 30 2008
|
|
|
REFERENCES
| Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
|
|
|
FORMULA
| E.g.f.: exp(x)*BesselI(0, 4*x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 20 2003
a(n) is also the central coefficient of (4+x+x^2)^n; a(n)=sum_{k=0..n} 3^(n-k) C(n,k) T(k,n), where T(k,n) is the triangle of trinomial coefficients = Coefficient of x^n of (1+x+x^2)^k : A027907 - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Mar 30 2008
a(n) = (1/Pi)*integral(x=-2..2, (2*x+1)^n/sqrt((2-x)*(2+x))). [Peter Luschny, Sep 12 2011]
|
|
|
PROG
| (PARI) for(n=0, 30, t=polcoeff((1+x+4*x^2)^n, n, x); print1(t", "))
|
|
|
CROSSREFS
| Cf. A002426, A084600-A084604, A084606-A084615.
Sequence in context: A139818 A146365 A146373 * A098773 A089998 A014728
Adjacent sequences: A084602 A084603 A084604 * A084606 A084607 A084608
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jun 01 2003
|
| |
|
|
