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A234570
7*binomial(10*n+7,n)/(10*n+7).
9
1, 7, 91, 1470, 26565, 514206, 10426416, 218618940, 4701550770, 103134123820, 2298706645235, 51909777109596, 1185134654128425, 27309853977084000, 634361032466470620, 14837590383963667320, 349163392095422769942, 8260872214482785042145, 196380752260155290992675
OFFSET
0,2
COMMENTS
Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=10, r=7.
LINKS
J-C. Aval, Multivariate Fuss-Catalan Numbers, arXiv:0711.0906v1, Discrete Math., 308 (2008), 4660-4669.
Thomas A. Dowling, Catalan Numbers Chapter 7
Wojciech Mlotkowski, Fuss-Catalan Numbers in Noncommutative Probability, Docum. Mathm. 15: 939-955.
FORMULA
G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=10, r=7.
MATHEMATICA
Table[7 Binomial[10 n + 7, n]/(10 n + 7), {n, 0, 30}]
PROG
(PARI) a(n) = 7*binomial(10*n+7, n)/(10*n+7);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(10/7))^7+x*O(x^n)); polcoeff(B, n)}
(Magma) [7*Binomial(10*n+7, n)/(10*n+7): n in [0..30]];
KEYWORD
nonn
AUTHOR
Tim Fulford, Dec 28 2013
STATUS
approved