|
|
A233908
|
|
10*binomial(7*n+10,n)/(7*n+10).
|
|
6
|
|
|
1, 10, 115, 1450, 19425, 271502, 3915100, 57821940, 870238200, 13298907050, 205811513765, 3218995093860, 50802419972395, 808016193159000, 12938696992921000, 208419656266988904, 3374960506795660365, 54907659530154222000, 897060906625956765000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=7, r=10.
|
|
LINKS
|
|
|
FORMULA
|
72*n*(6*n+5)*(3*n+5)*(2*n+3)*(3*n+4)*(6*n+7)*a(n) -7*(7*n+4)*(7*n+8)*(7*n+5)*(7*n+9)*(7*n+6)*(7*n+3)*a(n-1)=0. - R. J. Mathar, Dec 22 2013
G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=7, r=10.
|
|
MATHEMATICA
|
Table[10 Binomial[7 n + 10, n]/(7 n + 10), {n, 0, 40}] (* Vincenzo Librandi, Dec 23 2013 *)
|
|
PROG
|
(PARI) a(n) = 10*binomial(7*n+10, n)/(7*n+10);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(7/10))^10+x*O(x^n)); polcoeff(B, n)}
(Magma) [10*Binomial(7*n+10, n)/(7*n+10): n in [0..30]]; // Vincenzo Librandi, Dec 23 2013
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|