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

Author

Christian G. Bower, Jun 09 2000

Keywords

• nonn

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]

Crossrefs

Cf. A055889, A000142.

Programs

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 */