A030015 Binomial transform of {1, primes}.

1, 3, 8, 21, 54, 137, 342, 837, 2006, 4713, 10882, 24771, 55764, 124465, 275934, 608283, 1334120, 2911871, 6325092, 13674121, 29425308, 63042233, 134517426, 285984131, 606056546, 1280778343, 2700105566, 5680099085, 11925792492, 24993841655, 52291456452

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• N. J. A. Sloane, Transforms

Crossrefs

Cf. A008578, A050513.

Programs

Mathematica

Flatten[{1, Table[1 + Sum[Binomial[n, k]*Prime[k], {k, 1, n}], {n, 1, 30}]}] (* Vaclav Kotesovec, Oct 29 2017 *)

Formula

G.f.: Prime(x/(1-x)), Prime(x) = Sum_{n>0} A008578(n)*x^n. - Vladimir Kruchinin, Aug 11 2010