A213907 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).

1, 3, 9, 34, 61, 261, 709, 1324, 4937, 15040, 28561, 107262, 248341, 522445, 1972363, 7591936, 8835345, 26421129, 145475533, 183752250, 701184621, 2234736295, 2996725227, 15105451596, 32483720761, 77618520551, 217809217211, 625456400842, 1638545943301

Offset: 0

Author

Paul D. Hanna, Jun 24 2012

Keywords

• nonn

Examples

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

Crossrefs

Cf. A075885.

Programs

PARI

{a(n)=1+sum(m=1, 2*n, prod(k=1, m, round(n/k)))}
for(n=0, 60, print1(a(n), ", "))