OFFSET
0,5
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
MATHEMATICA
Table[Sum[(-1)^(n-k)Floor[Sqrt[Binomial[2k, k]/(k+1)]], {k, 0, n}], {n, 0, 40}]
RecurrenceTable[{a[0] == 1, a[n] == Floor[Sqrt[CatalanNumber[n]]] - a[n - 1]}, a, {n, 30}] (* Jon Maiga, Nov 16 2018 *)
PROG
(Maxima) makelist(sum((-1)^(n-k)*floor(sqrt(binomial(2*k, k)/(k+1))), k, 0, n), n, 0, 24);
(PARI) vector(40, n, n--; sum(k=0, n, (-1)^(n-k)*floor( sqrt(binomial(2*k, k)/(k+1))))) \\ G. C. Greubel, Nov 16 2018
(Magma) [(&+[(-1)^(n-k)*Floor(Sqrt(Binomial(2*k, k)/(k+1))): k in [0..n]]) : n in [0..40]]; // G. C. Greubel, Nov 16 2018
(Sage) [sum((-1)^(n-k+1)*floor(sqrt(binomial(2*k, k)/(k+1))) for k in range(n)) for n in (1..40)] # G. C. Greubel, Nov 16 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Jul 07 2011
STATUS
approved