|
| |
|
|
A132306
|
|
a(n) = Sum_{k=0..2n-1} C(2n-1,k)*trinomial(n,k) for n>0 with a(0)=1.
|
|
1
| |
|
|
1, 2, 18, 179, 1874, 20202, 221943, 2470827, 27777618, 314642708, 3585365618, 41054041602, 471980219543, 5444542749674, 62987391100239, 730515277512729, 8490829425196626, 98878672140171984, 1153433769999190212
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
FORMULA
| a(n) = Sum_{k=0..2n} C(2n,k)*trinomial(n,k)/2 for n>0 with a(0)=1 ; also, a(n) = Sum_{k=0..2n} C(-2n-1,k)*trinomial(n,k)/2 for n>0 with a(0)=1 ; also, a(n) = Sum_{k=0..2n} C(-2n,k)*trinomial(n,k) ; where trinomial(n,k) = [x^k] (1 + x + x^2)^n.
|
|
|
PROG
| (PARI) {a(n)=sum(k=0, 2*n, binomial(2*n-1, k)*polcoeff((1+x+x^2)^n, k))} (PARI) {a(n)=if(n==0, 1, sum(k=0, 2*n, binomial(2*n, k)*polcoeff((1+x+x^2)^n, k))/2)} (PARI) {a(n)=if(n==0, 1, sum(k=0, 2*n, binomial(-2*n-1, k)*polcoeff((1+x+x^2)^n, k))/2)} (PARI) {a(n)=sum(k=0, 2*n, binomial(-2*n, k)*polcoeff((1+x+x^2)^n, k))}
|
|
|
CROSSREFS
| Cf. A082759.
Sequence in context: A052665 A092473 A073558 * A099044 A161122 A019581
Adjacent sequences: A132303 A132304 A132305 * A132307 A132308 A132309
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 18 2007
|
| |
|
|
