A213907 - OEIS

%I #8 Dec 16 2024 14:35:54

%S 1,3,9,34,61,261,709,1324,4937,15040,28561,107262,248341,522445,

%T 1972363,7591936,8835345,26421129,145475533,183752250,701184621,

%U 2234736295,2996725227,15105451596,32483720761,77618520551,217809217211,625456400842,1638545943301

%N a(n) = 1 + n + n*{n/2} + n*{n/2}*{n/3} + n*{n/2}*{n/3}*{n/4} +... where {x} = [x+1/2] = round(x).

%e a(2) = 1 + 2 + 2*1 + 2*1*1 + 2*1*1*1 = 9.

%e a(3) = 1 + 3 + 3*2 + 3*2*1 + 3*2*1*1 + 3*2*1*1*1 + 3*2*1*1*1*1 = 34.

%o (PARI) {a(n)=1+sum(m=1, 2*n, prod(k=1, m, round(n/k)))}

%o for(n=0, 60, print1(a(n), ", "))

%Y Cf. A075885.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jun 24 2012