OFFSET
0,2
COMMENTS
Invert transform of the odd primes.
Number of compositions (ordered partitions) of n where there are prime(k+1) sorts of part k.
LINKS
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72. Erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
N. J. A. Sloane, Transforms
FORMULA
G.f.: 1/(1 - Sum_{k>=1} prime(k+1)*x^k).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Prime[k + 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 25}]
nmax = 25; CoefficientList[Series[1/(1 - Sum[Prime[k + 1] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
PROG
(PARI) t=26; Vec(1/(1-sum(k=1, t, prime(k+1)*x^k)) + O(x^t)) \\ Felix Fröhlich, Sep 22 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 22 2017
STATUS
approved