A234570 7*binomial(10*n+7,n)/(10*n+7).

1, 7, 91, 1470, 26565, 514206, 10426416, 218618940, 4701550770, 103134123820, 2298706645235, 51909777109596, 1185134654128425, 27309853977084000, 634361032466470620, 14837590383963667320, 349163392095422769942, 8260872214482785042145, 196380752260155290992675

Offset: 0

Author

Tim Fulford, Dec 28 2013

Keywords

• nonn

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=10, r=7.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• 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.

Crossrefs

Cf. A000108, A059968, A234525, A234526, A234527, A234528, A234529, A234571, A234573, A229963.

Programs

Magma

[7*Binomial(10*n+7, n)/(10*n+7): n in [0..30]];

Mathematica

Table[7 Binomial[10 n + 7, n]/(10 n + 7), {n, 0, 30}]

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)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=10, r=7.