A307772 Expansion of e.g.f. Sum_{k>=1} prime(k)*log(1 + x)^k/k!.

2, 1, 0, -2, 14, -100, 792, -6984, 68112, -728924, 8498662, -107269546, 1457660932, -21221947564, 329615120330, -5440973779098, 95131744001392, -1756450890029772, 34152285999547328, -697588907138104978, 14934641645024407092, -334433142861340604942, 7818455679081107296154

Offset: 1

Author

Ilya Gutkovskiy, Apr 27 2019

Keywords

• sign

Comments

Inverse Stirling transform of primes.

Links

• Eric Weisstein's World of Mathematics, Stirling Transform

Crossrefs

Cf. A000040, A085507, A307771, A307773.

Programs

Mathematica

nmax = 23; Rest[CoefficientList[Series[Sum[Prime[k] Log[1 + x]^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!]
Table[Sum[StirlingS1[n, k] Prime[k], {k, 1, n}], {n, 1, 23}]

Formula

a(n) = Sum_{k=1..n} Stirling1(n,k)*prime(k).