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A234043 a(n) = C(5*(n+1),4)/5, with n >= 0. 8
1, 42, 273, 969, 2530, 5481, 10472, 18278, 29799, 46060, 68211, 97527, 135408, 183379, 243090, 316316, 404957, 511038, 636709, 784245, 956046, 1154637, 1382668, 1642914, 1938275, 2271776, 2646567, 3065923, 3533244, 4052055 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Used as one of the 5-section parts of A234042.

The Fuss-Catalan numbers are Cat(d,k)= [1/(k*(d-1)+1)]*binomial(k*d,k) and enumerate the number of (d+1)-gon partitions of a (k*(d-1)+2)-gon (cf. Whieldon and Schuetz link). a(n)= Cat(n,5) (Offset=1), so enumerates the number of (n+1)-gon partitions of a (5*(n-1)+2)-gon. Analogous series are A000326 (k=3) and A100157 (k=4). - Tom Copeland, Oct 05 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Alison Schuetz and Gwyneth Whieldon, Polygonal Dissections and Reversions of Series, arXiv:1401.7194 [math.CO], 2014.

FORMULA

G.f: (1 + 37*x + 73*x^2 + 14*x^3)/(1-x)^5.

a(n) = A234042(5*n+1) for n >= 0.

a(n) = (n+1)*(5*n+2)*(5*n+3)*(5*n+4)/24.

MATHEMATICA

CoefficientList[Series[(1 + 37 x + 73 x^2 + 14 x^3)/(1 - x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Feb 26 2014 *)

PROG

(MAGMA) [Binomial(5*(n+1), 4)/5: n in [0..40]]; // Vincenzo Librandi, Feb 26 2014

CROSSREFS

Cf. A151989, A234042.

Sequence in context: A156357 A300338 A064369 * A323800 A309925 A188058

Adjacent sequences:  A234040 A234041 A234042 * A234044 A234045 A234046

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Feb 24 2014

STATUS

approved

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Last modified March 3 13:15 EST 2021. Contains 341762 sequences. (Running on oeis4.)