|
|
A370273
|
|
Coefficient of x^n in the expansion of 1/( (1-x)^2 * (1-x^3) )^n.
|
|
1
|
|
|
1, 2, 10, 59, 362, 2277, 14581, 94572, 619242, 4084538, 27099435, 180651913, 1209036725, 8118629365, 54671662692, 369071775684, 2496852123882, 16923762715911, 114902801532622, 781296976824693, 5319705042364587, 36265061394634215, 247497082392976415
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(3*n-3*k-1,n-3*k).
The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x)^2 * (1-x^3) ). See A369297.
|
|
PROG
|
(PARI) a(n, s=3, t=1, u=2) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((u+1)*n-s*k-1, n-s*k));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|