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A233658 7*binomial(4*n + 7, n)/(4*n + 7). 4
1, 7, 49, 357, 2695, 20930, 166257, 1344904, 11042724, 91801255, 771201431, 6536904290, 55838330730, 480197194260, 4154140621425, 36126361733616, 315647802951628, 2769544822393356, 24392874398953060, 215582307059144025, 1911286446370861455, 16993580092566979770, 151491588134469616215 (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=4, 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.

FORMULA

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=4, r=7.

MATHEMATICA

Table[7 Binomial[4 n + 7, n]/(4 n + 7), {n, 0, 30}]

PROG

(PARI) a(n) = 7*binomial(4*n+7, n)/(4*n+7);

(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(4/7))^7+x*O(x^n)); polcoeff(B, n)}

(MAGMA) [7*Binomial(4*n+7, n)/(4*n+7): n in [0..30]];

CROSSREFS

Cf. A000108, A002293, A069271, A006632, A196678, A006633, A233666, A006634, A233667.

Sequence in context: A024582 A024587 A240721 * A144820 A199554 A221462

Adjacent sequences:  A233655 A233656 A233657 * A233659 A233660 A233661

KEYWORD

nonn,easy

AUTHOR

Tim Fulford, Dec 14 2013

STATUS

approved

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Last modified December 15 22:53 EST 2018. Contains 318157 sequences. (Running on oeis4.)