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A118971 a(n) = 4*binomial(5*n+3,n)/(4*n+4). 17
1, 4, 26, 204, 1771, 16380, 158224, 1577532, 16112057, 167710664, 1772645420, 18974357220, 205263418941, 2240623268512, 24648785802336, 272994644359580, 3041495503591365, 34064252968167180, 383302465665133014 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A quadrisection of A118968.

For n >= 1, a(n-1) is the number of lattice paths from (0,0) to (4n,n) using only the steps (1,0) and (0,1) and which stay strictly below the line y = x/4 except at the path's endpoints. -  Lucas A. Brown, Aug 21 2020

LINKS

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

Paul Barry, Characterizations of the Borel triangle and Borel polynomials, arXiv:2001.08799 [math.CO], 2020.

Elżbieta Liszewska, Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.

FORMULA

G.f.: If the inverse series of y*(1-y)^4 is G(x) then A(x)=G(x)/x.

D-finite with recurrnce 8*(4*n+1)*(2*n+1)*(4*n+3)*(n+1)*a(n) -5*(5*n+1)*(5*n+2)*(5*n+3)*(5*n-1)*a(n-1)=0. - R. J. Mathar, Nov 26 2012

a(n) = (4/5)*binomial(5*(n+1),n+1)/(5*(n+1)-1). - Bruno Berselli, Jan 17 2014

E.g.f.: 4F4(4/5,6/5,7/5,8/5; 5/4,3/2,7/4,2; 3125*x/256). - Ilya Gutkovskiy, Jan 23 2018

G,f.: 5F4(4/5, 5/5, 6/5, 7/5, 8/5; 5/4, 6/4, 7/4, 8/4; (5^5/4^4)*x). - Wolfdieter Lang, Feb 06 2020

MATHEMATICA

Table[4*Binomial[5n+3, n]/(4n+4), {n, 0, 30}] (* Harvey P. Dale, Apr 09 2012 *)

CROSSREFS

Cf. A006632, A130564, A130565, A234466 (members of the same family).

Sequence in context: A246509 A253255 A141381 * A124554 A321586 A206391

Adjacent sequences:  A118968 A118969 A118970 * A118972 A118973 A118974

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 07 2006

STATUS

approved

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Last modified September 17 01:53 EDT 2021. Contains 347478 sequences. (Running on oeis4.)