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A233743 a(n) = 7*binomial(6*n + 7, n)/(6*n + 7). 10
1, 7, 63, 644, 7105, 82467, 992446, 12271512, 154962990, 1990038435, 25909892008, 341225775072, 4537563627415, 60842326873230, 821692714673340, 11167153485624304, 152610018401940330, 2095863415900961490, 28910564819681953485, 400379714692751795820 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Fuss-Catalan sequence is a(n,p,r) = r*binomial(n*p + r, n)/(n*p + r); this is the case p = 6, r = 7.

LINKS

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

J-C. Aval, Multivariate Fuss-Catalan Numbers, arXiv:0711.0906 [math.CO], 2007.

J-C. Aval, Multivariate Fuss-Catalan Numbers, 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.

Wikipedia, Fuss-Catalan number

FORMULA

G.f. satisfies: A(x) = {1 + x*A(x)^(p/r)}^r, where p = 6, r = 7.

From _Peter Bala, Oct 16 2015: (Start)

O.g.f. A(x) = 1/x * series reversion (x*C(-x)^7), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. for the Catalan numbers A000108. See cross-references for other Fuss-Catalan sequences with o.g.f. 1/x * series reversion (x*C(-x)^k), k = 3 through 11.

A(x)^(1/7) is the o.g.f. for A002295. (End)

MATHEMATICA

Table[7 Binomial[6 n + 7, n]/(6 n + 7), {n, 0, 40}] (* Vincenzo Librandi, Dec 16 2013 *)

PROG

(PARI) a(n) = 7*binomial(6*n+7, n)/(6*n+7);

(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(6/7))^7+x*O(x^n)); polcoeff(B, n)}

(MAGMA) [7*Binomial(6*n+7, n)/(6*n+7): n in [0..30]]; // Vincenzo Librandi, Dec 16 2013

CROSSREFS

Cf. A000108, A002295, A212071, A212072, A212073, A130564, A233827, A233829, A233830.

Cf. A000245 (k = 3), A006629 (k = 4), A196678 (k = 5), A233668 (k = 6), A233835 (k = 8), A234467 (k = 9), A232265 (k = 10), A229963 (k = 11).

Sequence in context: A155132 A270472 A266426 * A015684 A051579 A185106

Adjacent sequences:  A233740 A233741 A233742 * A233744 A233745 A233746

KEYWORD

nonn,easy

AUTHOR

Tim Fulford, Dec 15 2013

EXTENSIONS

More terms from Vincenzo Librandi, Dec 16 2013

STATUS

approved

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Last modified November 13 08:18 EST 2019. Contains 329093 sequences. (Running on oeis4.)