|
| |
|
|
A121677
|
|
a(n) = A121676(n)/(n+1) = [x^n] (1 + x*(1+x)^(n-1) )^(n+1) / (n+1).
|
|
1
| |
|
|
1, 1, 2, 8, 50, 402, 3932, 45075, 588450, 8580542, 137799497, 2410575026, 45531000715, 921946835474, 19895218322982, 455271977561120, 11000793881924130, 279648297003419318, 7454931579222301709
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
FORMULA
| a(n) = Sum_{k=0..n+1} C(n+1,k) * C((n-1)*k,n-k) / (n+1).
|
|
|
EXAMPLE
| At n=4, a(4) = [x^4] (1 + x*(1+x)^3 )^5/5 = 250/5 = 50, since
(1 + x*(1+x)^3 )^5 = 1 + 5*x + 25*x^2 + 85*x^3 + 250*x^4 +...
|
|
|
PROG
| (PARI) a(n)=sum(k=0, n+1, binomial(n+1, k)*binomial((n-1)*k, n-k))/(n+1)
|
|
|
CROSSREFS
| Cf. A121676; variants: A121673-A121675, A121678-A121680.
Sequence in context: A027047 A034491 A186182 * A120956 A000557 A193352
Adjacent sequences: A121674 A121675 A121676 * A121678 A121679 A121680
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 15 2006
|
| |
|
|
