The On-Line Encyclopedia of Integer Sequences (OEIS)

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A234510

a(n) = 7*binomial(9*n+7,n)/(9*n+7).
(history; published version)

#24 by Charles R Greathouse IV at Thu Sep 08 08:46:06 EDT 2022

PROG

(MAGMAMagma) [7*Binomial(9*n+7, n)/(9*n+7): n in [0..30]]; // Vincenzo Librandi, Dec 27 2013

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#23 by Bruno Berselli at Wed Oct 14 06:38:21 EDT 2015

STATUS

editing

approved

#22 by Bruno Berselli at Wed Oct 14 06:38:17 EDT 2015

NAME

a(n) = 7*binomial(9*n+7,n)/(9*n+7).

STATUS

proposed

editing

#21 by Peter Bala at Wed Oct 14 06:30:47 EDT 2015

STATUS

editing

proposed

#20 by Peter Bala at Wed Oct 14 06:18:54 EDT 2015

COMMENTS

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p = 9, r = 7.

LINKS

Wikipedia, <a href="https://en.wikipedia.org/wiki/Fuss-Catalan_number">Fuss-Catalan number</a>

FORMULA

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p = 9, r = 7.

O.g.f. A(x) = 1/x * series reversion (x/C(x)^7), where C(x) is the o.g.f. for the Catalan numbers A000108. A(x)^(1/7) is the o.g.f. for A062994. - Peter Bala, Oct 14 2015

CROSSREFS

Cf. A000108, A143554, A234505, A234506, A234507, A234508, A234509, A234513, A232265, A062994, A069271, A118970, A212073, A233834, A234465, A234571, A235339.

KEYWORD

nonn,easy

STATUS

approved

editing

#19 by N. J. A. Sloane at Fri Jan 10 19:15:58 EST 2014

STATUS

proposed

approved

#18 by Tim Fulford at Fri Jan 10 11:23:39 EST 2014

STATUS

editing

proposed

#17 by Tim Fulford at Fri Jan 10 11:23:18 EST 2014

COMMENTS

Fuss-Catalan sequence is a(n,p,r,s) = sr*binomial(nrnp+s,r,n)/(nrnp+s), this is the case s=7, r), where p=9, r=7.

LINKS

J-C. Aval, <a href="http://www.labriarxiv.fr/persoorg/avalpdf/b50711.0906v1.pdf"> Multivariate Fuss-Catalan Numbers</a>, arXiv:0711.0906v1, Discrete Math., 308 (2008), 4660-4669.

Wojciech Mlotkowski, <a href="http://www.math.uiuc.edu/documenta/vol-15/28.pdf">Fuss-Catalan Numbers in Noncommutative Probability</a>, Docum. Mathm. 15: 939-955.

FORMULA

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=9, r=7.

PROG

(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(9/7))^7+x*O(x^n)); polcoeff(B, n)}

CROSSREFS

Cf. A000108, A143554, A234505, A234506, A234507, A234508, A234509, A234513, A232265.

STATUS

approved

editing

Discussion

Fri Jan 10

11:23

Tim Fulford: improved links and added Gf.  Regards, Tim

#16 by Bruno Berselli at Fri Dec 27 19:06:30 EST 2013

STATUS

editing

approved

#15 by Bruno Berselli at Fri Dec 27 19:06:10 EST 2013

NAME

7*binomial(9*n+7,n)/(9*n+7).

DATA

1, 7, 84, 1232, 20090, 349860, 6371764, 119877472, 2311664355, 45448324110, 907580289616, 18358110017520, 375353605696524, 7744997102466932, 161070300819384000, 3372697621463787456, 71046594621639707245, 1504569659175026591805, 32013490616435232789192

STATUS

proposed

editing