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A235340 10*binomial(11*n+10,n)/(11*n+10). 3
1, 10, 155, 2870, 58565, 1270752, 28765650, 671650110, 16057800980, 391139588190, 9672348219898, 242182964452000, 6127720969229265, 156431295179478200, 4024231652469275640, 104218796026870015374, 2714941275486017847825 (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=11, r=10.

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

Elżbieta Liszewska, Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.

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, here p=11, r=10.

MATHEMATICA

Table[10 Binomial[11 n + 10, n]/(11 n + 10), {n, 0, 30}]

PROG

(PARI) a(n) = 10*binomial(11*n+10, n)/(11*n+10);

(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/10))^10+x*O(x^n)); polcoeff(B, n)}

(MAGMA) [10*Binomial(11*n+10, n)/(11*n+10): n in [0..30]];

CROSSREFS

Cf. A230388, A234868, A234869, A234870, A234871, A234872, A234873, A235338, A235339.

Sequence in context: A292837 A261802 A246239 * A306034 A129460 A200989

Adjacent sequences:  A235337 A235338 A235339 * A235341 A235342 A235343

KEYWORD

nonn

AUTHOR

Tim Fulford, Jan 06 2014

STATUS

approved

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Last modified October 22 16:15 EDT 2021. Contains 348174 sequences. (Running on oeis4.)