A307899 -id:A307899 - cp's OEIS frontend

A307898 Expansion of 1/(1 - x * Sum_{k>=1} prime(k)*x^k).

1, 0, 2, 3, 9, 19, 48, 107, 258, 594, 1405, 3277, 7693, 18004, 42203, 98834, 231592, 542497, 1271003, 2977529, 6975674, 16342011, 38285178, 89691782, 210124363, 492265243, 1153247379, 2701752062, 6329489153, 14828313076, 34738805240, 81383803849, 190660665579, 446667359857, 1046423138962

Offset: 0

Ilya Gutkovskiy, May 04 2019

nonn

Antidiagonal sums of square array, in which row m equals the m-fold convolution of primes with themselves.

Cf. A000040, A030017, A030018, A300662, A307899.

nmax = 34; CoefficientList[Series[1/(1 - x Sum[Prime[k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[Prime[k] a[n - k - 1], {k, 1, n - 1}]; Table[a[n], {n, 0, 34}]

Recurrence: a(n+1) = Sum_{k=1..n} prime(k)*a(n-k).

A353156 a(0) = 1; a(n) = -Sum_{k=1..n} prime(k+1) * a(n-k).

Original entry on oeis.org

1, -3, 4, -4, 2, 6, -22, 46, -74, 86, -40, -120, 450, -958, 1506, -1694, 744, 2500, -9184, 19422, -30450, 34032, -14178, -52286, 188038, -394724, 615102, -681110, 268666, 1089974, -3847390, 8021030, -12426638, 13632728, -5063588, -22711916, 78708912, -162966020, 251005706

Offset: 0

Ilya Gutkovskiy, Apr 27 2022

sign

Cf. A006005, A030017, A030018, A065091, A292744, A300662, A307898, A307899, A346792.

a[0] = 1; a[n_] := a[n] = -Sum[Prime[k + 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 38}]
nmax = 38; CoefficientList[Series[1/(1 + Sum[Prime[k + 1] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

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

cp's OEIS Frontend

A307898 Expansion of 1/(1 - x * Sum_{k>=1} prime(k)*x^k).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula