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A158267
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Inverse Euler transform of A156305.
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0
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1, 4, 13, 59, 151, 916, 1961, 12035, 35110, 166204, 384781, 3154367, 5600323, 34384676, 124093963, 582290595, 1235438587, 9831378712, 18602770421, 144738772109, 410101237013, 1721535323380, 4295702988313, 40309503022439
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OFFSET
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1,2
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COMMENTS
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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).
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LINKS
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Table of n, a(n) for n=1..24.
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FORMULA
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a(n) = (1/n)*Sum_{d|n} sigma(d)*C(2d-1,d)*moebius(n/d).
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EXAMPLE
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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*...].
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MATHEMATICA
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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 *)
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PROG
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(PARI) {a(n)=(1/n)*sumdiv(n, d, sigma(d)*binomial(2*d-1, d)*moebius(n/d))}
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CROSSREFS
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Cf. A156305, A001700.
Sequence in context: A149484 A149485 A006798 * A219572 A026663 A149486
Adjacent sequences: A158264 A158265 A158266 * A158268 A158269 A158270
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Apr 09 2009
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STATUS
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approved
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