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A118970 a(n) = 3*binomial(5n+2,n)/(4n+3). 10
1, 3, 18, 136, 1155, 10530, 100688, 996336, 10116873, 104819165, 1103722620, 11777187240, 127067830773, 1383914371728, 15194457001440, 167996704221280, 1868870731122405, 20903064321375315, 234927317665726686 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A quadrisection of A118968.

Convolved with A118969 (1, 2, 11, 80, 665,...) = A002294: (1, 5, 35, 285, 2530,...) - Gary W. Adamson, Nov 07 2011

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..924

Henri Muehle, Philippe Nadeau, A Poset Structure on the Alternating Group Generated by 3-Cycles, arXiv:1803.00540 [math.CO], 2018.

FORMULA

G.f.: ogf(A002294)^3 - Mark van Hoeij, Apr 23 2013

8*n*(4*n+1)*(2*n+1)*(4*n+3)*a(n) -5*(5*n+1)*(5*n+2)*(5*n-2)*(5*n-1)*a(n-1)=0. - R. J. Mathar, Dec 02 2014

From Peter Bala, Oct 08 2015: (Start)

O.g.f. A(x) = 1/x * series reversion ( x/C(x)^3 ), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. for the Catalan numbers A000108.

1/3*x*A'(x)/A(x) = x + 9*x^2 + 91*x^3 + 969*x^4 + ... is the o.g.f. for A163456. (End)

MAPLE

ogf := series(RootOf(A = 1 + x * A^5, A)^3, x=0, 30); # Mark van Hoeij, Apr 22 2013

MATHEMATICA

Array[3 Binomial[5 # + 2, #]/(4 # + 3) &, 19, 0] (* Michael De Vlieger, May 30 2018 *)

PROG

(PARI) a(n)=3*binomial(5*n+2, n)/(4*n+3); \\ Joerg Arndt, Apr 23 2013

CROSSREFS

Cf. A118969, A002294, A000108, A163456.

Sequence in context: A177406 A289430 A247452 * A003122 A275549 A039618

Adjacent sequences:  A118967 A118968 A118969 * A118971 A118972 A118973

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 07 2006

STATUS

approved

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Last modified May 19 17:48 EDT 2019. Contains 323395 sequences. (Running on oeis4.)