A158267 Inverse Euler transform of A156305.

1, 4, 13, 59, 151, 916, 1961, 12035, 35110, 166204, 384781, 3154367, 5600323, 34384676, 124093963, 582290595, 1235438587, 9831378712, 18602770421, 144738772109, 410101237013, 1721535323380, 4295702988313, 40309503022439

Offset: 1

Author

Paul D. Hanna, Apr 09 2009

Keywords

• nonn

Comments

G.f. of A156305: exp( Sum_{n>=1} sigma(n)*C(2*n-1,n)*x^n/n ), where C(2n-1,n) = A001700(n-1).

Examples

			Let G(x) = g.f. of A156305:
G(x) = 1 + x + 5*x^2 + 18*x^3 + 87*x^4 + 290*x^5 + 1553*x^6 +...
G(x) = 1/[(1-x)*(1-x^2)^4*(1-x^3)^13*(1-x^4)^59*(1-x^5)^151*...].
		

Crossrefs

Cf. A156305, A001700.

Programs

Mathematica

Table[Sum[DivisorSigma[1, d]*Binomial[2*d - 1, d]*MoebiusMu[n/d], {d, Divisors[n]}] / n, {n, 1, 30}] (* Vaclav Kotesovec, Oct 09 2019 *)

PARI

{a(n)=(1/n)*sumdiv(n,d, sigma(d)*binomial(2*d-1, d)*moebius(n/d))}

Formula

a(n) = (1/n)*Sum_{d|n} sigma(d)*C(2d-1,d)*moebius(n/d).