OFFSET
0,3
COMMENTS
Greatest multiplicity of one- or two-dimensional standard representation of Lie algebras sl(2) in decomposition of tensor power F6^k, where F6 is the standard 6-dimensional irreducible representation of sl(2). - Leonid Bedratyuk, Jul 22 2004
Sum_{k=0..floor(5*n/12)} (-1)^k*binomial(n,k)*binomial(n + floor(5*n/2) - 6*k - 1, n-1). - Warut Roonguthai, May 21 2006
LINKS
T. D. Noe, Table of n, a(n) for n = 0..200
Vaclav Kotesovec, Recurrence
FORMULA
a(n) ~ 6^n * sqrt(6/(35*Pi*n)). - Vaclav Kotesovec, Aug 09 2013
EXAMPLE
Number of ways of getting most likely sum using n 6-sided dice (e.g., for n=2, 7 is the most prevalent sum and there are 6 different ways to get it: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1).
MAPLE
sum((-1)^(k)*binomial(n, k)*binomial(n+floor(5*n/2)-6*k-1, n-1), k=0..floor(5*n/12)); # Warut Roonguthai, May 21 2006
MATHEMATICA
Flatten[{1, Table[Coefficient[Expand[Sum[x^j, {j, 0, 5}]^n], x^Floor[5*n/2]], {n, 1, 20}]}] (* Vaclav Kotesovec, Aug 09 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonn Dalton jdalton(AT)vnet.ibm.com
STATUS
approved