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

0,3

Comments

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

Links

Table of n, a(n) for n=0..34.

Formula

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

Mathematica

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}]

Crossrefs

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

Sequence in context: A094679 A298357 A094812 * A079992 A324374 A106519

Adjacent sequences: A307895 A307896 A307897 * A307899 A307900 A307901

Keyword

nonn

Author

Ilya Gutkovskiy, May 04 2019

Status

approved