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

0,3

Links

Table of n, a(n) for n=0..29.

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]

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 *)

Prog

(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 */

Crossrefs

Cf. A055889, A000142.

Sequence in context: A132891 A200544 A308448 * A306884 A219768 A038359

Adjacent sequences: A055887 A055888 A055889 * A055891 A055892 A055893

Keyword

nonn

Author

Christian G. Bower, Jun 09 2000

Status

approved