|
| |
|
|
A369262
|
|
Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+x^2)^3 ).
|
|
4
|
|
|
|
1, 1, 5, 17, 80, 363, 1792, 8969, 46319, 242994, 1296046, 6996163, 38175142, 210162728, 1166020560, 6512854409, 36593709385, 206686641555, 1172856064443, 6683348391034, 38228129813288, 219411037878578, 1263245957786120, 7293833100110787, 42224142505632305
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+3,k) * binomial(2*n-2*k,n-2*k).
a(n) = (1/(n+1)) * [x^n] ( 1/(1-x) * (1+x^2)^3 )^(n+1). - Seiichi Manyama, Feb 14 2024
|
|
|
PROG
|
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)/(1+x^2)^3)/x)
(PARI) a(n, s=2, t=3, u=1) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
