A336185 - OEIS

A336185

a(n) = prime(n) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * k * a(k) * prime(n-k).

2, 7, 39, 314, 3379, 45440, 733335, 13807364, 297105507, 7192224540, 193452015049, 5723688147650, 184742675924105, 6459822765521016, 243253254143586291, 9814313764465482774, 422366963490734937123, 19312961877700115922410, 935042624229107088382095

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..19.

FORMULA

E.g.f.: -log(1 - Sum_{k>=1} prime(k) * x^k / k!).

MATHEMATICA

a[n_] := a[n] = Prime[n] + (1/n) Sum[Binomial[n, k] k a[k] Prime[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 19}]

nmax = 19; CoefficientList[Series[-Log[1 - Sum[Prime[k] x^k/k!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]! // Rest

CROSSREFS

Cf. A000040, A007446, A007447, A307770.

Sequence in context: A060073 A322152 A368927 * A187806 A369196 A300519

Adjacent sequences: A336182 A336183 A336184 * A336186 A336187 A336188

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 10 2020

STATUS

approved