A055890 CIK transform of partition numbers A000041.
1, 1, 3, 6, 14, 28, 68, 148, 358, 845, 2061, 5018, 12458, 30922, 77557, 195154, 493809, 1253614, 3195210, 8166758, 20935826, 53799072, 138571332, 357647566, 924846881, 2395702829, 6215779536, 16150985916, 42024260088, 109485000778
Offset: 0
Keywords
Links
- C. G. Bower, Transforms (2)
- P. Flajolet and M. Soria, The Cycle Construction. In SIAM J. Discr. Math., vol. 4 (1), 1991, pp. 58-60.
- P. Flajolet and M. Soria, The Cycle Construction. [pdf file]
Programs
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Mathematica
nmax = 30; f[x_] = 1/Product[1 - x^n, {n, 1, nmax}] - 1; gf = 1+Sum[(EulerPhi[n]/n)*Log[1/(1 - f[x^n])] + O[x]^nmax, {n, 1, nmax}]; CoefficientList[gf, x] (* Jean-François Alcover, Jul 29 2018, from PARI *) -
PARI
N = 66; x = 'x + O('x^N); f(x) = 1 / prod(n=1,N, 1-x^n ) - 1; \\ A055890 gf = 1 + sum(n=1,N, eulerphi(n)/n*log(1/(1-f(x^n))) ); v = Vec(gf) /* Joerg Arndt, Jan 21 2013 */