A079589 a(n) = C(5n+1,n).

1, 6, 55, 560, 5985, 65780, 736281, 8347680, 95548245, 1101716330, 12777711870, 148902215280, 1742058970275, 20448884000160, 240719591939480, 2840671544105280, 33594090947249085, 398039194165652550

Offset

0,2

Comments

a(n) is the number of paths from (0,0) to (5n,n) taking north and east steps while avoiding exactly 2 consecutive north steps. - Shanzhen Gao, Apr 15 2010

References

Shanzhen Gao, Pattern Avoidance in Paths and Walks, in preparation [From Shanzhen Gao, Apr 15 2010]

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) is asymptotic to c*sqrt(n)*(3125/256)^n with c=0.557.... [c = 5^(3/2)/(sqrt(Pi)*2^(7/2)) = 0.55753878629774... - Vaclav Kotesovec, Feb 14 2019]

8*n*(4*n+1)*(2*n-1)*(4*n-1)*a(n) -5*(5*n+1)*(5*n-3)*(5*n-2)*(5*n-1)*a(n-1)=0. - R. J. Mathar, Jul 17 2014

G.f.: hypergeom([2/5, 3/5, 4/5, 6/5], [1/2, 3/4, 5/4], (3125/256)*x). - Robert Israel, Aug 07 2014

a(n) = [x^n] 1/(1 - x)^(2*(2*n+1)). - Ilya Gutkovskiy, Oct 10 2017

Maple

seq(binomial(5*n+1, n), n=0..100); # Robert Israel, Aug 07 2014

Mathematica

Table[Binomial[5n+1, n], {n, 0, 20}]  (* Harvey P. Dale, Jan 23 2011 *)

Prog

(Magma) [Binomial(5*n+1, n): n in [0..20]]; // Vincenzo Librandi, Aug 07 2014

Crossrefs

Cf. A052203.

Sequence in context: A110431 A121661 A118836 * A371776 A372210 A365840

Adjacent sequences: A079586 A079587 A079588 * A079590 A079591 A079592

Keyword

nonn

Author

Benoit Cloitre, Jan 26 2003

Status

approved