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

1,2

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).

Links

Table of n, a(n) for n=1..24.

Formula

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

Example

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*...].

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 *)

Prog

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

Crossrefs

Cf. A156305, A001700.

Sequence in context: A149484 A149485 A006798 * A219572 A026663 A149486

Adjacent sequences: A158264 A158265 A158266 * A158268 A158269 A158270

Keyword

nonn

Author

Paul D. Hanna, Apr 09 2009

Status

approved