

A118971


a(n) = binomial(5*n+3,n)/(n+1).


23



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

For n >= 1, a(n1) 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
This is instance k = 4 of the family {c(k, n+1)}_{n>=0} given in a comment in A130564.  Wolfdieter Lang, Feb 04 2024


LINKS



FORMULA

G.f.: If the inverse series of y*(1y)^4 is G(x) then A(x)=G(x)/x.
Dfinite with recurrence 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*n1)*a(n1)=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([4,5,6,7,8]/5, [5,6,7,8]/4; (5^5/4^4)*x) = (4/(5*x))*(1  4F3([1,1,2,3]/5, [1,2,3]/4; (5^5/4^4)*x)).  Wolfdieter Lang, Feb 15 2024


MATHEMATICA

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


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



