OFFSET
0,2
COMMENTS
Generally (for p>1), partial sums of the binomial coefficients C(p*n,n) are asymptotic to (1/(1-(p-1)^(p-1)/p^p)) * sqrt(p/(2*Pi*n*(p-1))) * (p^p/(p-1)^(p-1))^n.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
Recurrence: 3*n*(3*n-2)*(3*n-1)*a(n) = (283*n^3 - 411*n^2 + 182*n - 24)*a(n-1) - 8*(2*n-1)*(4*n-3)*(4*n-1)*a(n-2).
a(n) ~ 2^(8*n+17/2)/(229*sqrt(Pi*n)*3^(3*n+1/2)).
MAPLE
A225612:=n->add(binomial(4*k, k), k=0..n): seq(A225612(n), n=0..30); # Wesley Ivan Hurt, Apr 01 2017
MATHEMATICA
Table[Sum[Binomial[4*k, k], {k, 0, n}], {n, 0, 20}]
Accumulate[Table[Binomial[4n, n], {n, 0, 20}]] (* Harvey P. Dale, Feb 01 2015 *)
PROG
(PARI) for(n=0, 50, print1(sum(k=0, n, binomial(4*k, k)), ", ")) \\ G. C. Greubel, Apr 01 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Aug 06 2013
STATUS
approved