A192186 - OEIS

%I #18 Nov 05 2025 08:48:58

%S 1,2,6,15,56,120,495,2002,4368,18564,38760,170544,735471,1562275,

%T 6906900,14307150,64512240,131128140,600805296,2707475148,5586853480,

%U 25518731280,51915526432,239877544005,1093260079344,2250829575120,10363194502115,21094923659355,97997533741800

%N a(n) = binomial(2*n, floor(n*sqrt(2))).

%H G. C. Greubel, <a href="/A192186/b192186.txt">Table of n, a(n) for n = 0..1000</a>

%t Table[Binomial[2*n, Floor[n*Sqrt[2]]], {n, 0, 50}] (* _G. C. Greubel_, Oct 05 2018 *)

%o (PARI) {a(n)=binomial(2*n, sqrtint(2*n^2))}

%o (Magma) [Binomial(2*n, Floor(n*Sqrt(2))) : n in [0..50]]; // _G. C. Greubel_, Oct 05 2018

%Y Cf. A001951, A135964 (binomial(floor(n*sqrt(2)), n)), A135965 (binomial(floor(n*(1+sqrt(2))), n)).

%K nonn,easy

%O 0,2

%A _Paul D. Hanna_, Jun 25 2011