OFFSET
0,2
COMMENTS
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..851
D. Merlini, R. Sprugnoli and M. C. Verri, The tennis ball problem, J. Combin. Theory, A 99 (2002), 307-344.
Rui Duarte and António Guedes de Oliveira, Short note on the convolution of binomial coefficients, arXiv:1302.2100 [math.CO], 2013.
FORMULA
a(n) = 3/5*(46656/3125)^n*(1+c/sqrt(n)+o(n^-1/2)) where c=0.388...
c = 8/(3*sqrt(15*Pi)) = 0.388461664210517... - Vaclav Kotesovec, May 25 2020
a(n) = sum(k=0,n,binomial(6*k+l,k)*binomial(6*(n-k)-l,n-k)) for every real number l. - Rui Duarte and António Guedes de Oliveira, Feb 16 2013
a(n) = sum(k=0,n,5^(n-k)*binomial(6n+1,k)). - Rui Duarte and António Guedes de Oliveira, Feb 17 2013
a(n) = sum(k=0,n,6^(n-k)*binomial(5n+k,k)) - Rui Duarte and António Guedes de Oliveira, Feb 17 2013
G.f.: hypergeom([1/6, 1/3, 1/2, 2/3, 5/6],[1/5, 2/5, 3/5, 4/5],46656*x/3125)^2. - Mark van Hoeij, Apr 19 2013
PROG
(PARI) a(n) = sum(k=0, n, 5^(n-k)*binomial(6*n+1, k));
vector(30, n, a(n-1)) \\ Altug Alkan, Sep 30 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Jan 26 2003
STATUS
approved