A292744 a(0) = 1; a(n) = Sum_{k=1..n} prime(k+1)*a(n-k).

1, 3, 14, 64, 294, 1346, 6166, 28242, 129362, 592538, 2714096, 12431808, 56943398, 260826950, 1194707382, 5472309246, 25065693008, 114812401444, 525893599720, 2408834540066, 11033569993066, 50538824799712, 231491059896394, 1060335514811206, 4856824295820082, 22246488881086116

Offset: 0

Author

Ilya Gutkovskiy, Sep 22 2017

Keywords

• nonn

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
• Index entries for sequences related to compositions

Crossrefs

Cf. A030017, A060801, A065091.

Programs

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]

PARI

t=26; Vec(1/(1-sum(k=1, t, prime(k+1)*x^k)) + O(x^t)) \\ Felix Fröhlich, Sep 22 2017

Formula

G.f.: 1/(1 - Sum_{k>=1} prime(k+1)*x^k).