Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #14 Sep 19 2023 01:50:25
%S 3,2,-2,6,-30,192,-1440,12240,-115916,1209422,-13784264,170426380,
%T -2272355448,32507854434,-496746974148,8076163535824,-139211242006108,
%U 2536169979011432,-48695473146705746,982863502262307532,-20805668315828056010,460926536131613987430
%N Inverse Stirling transform of odd primes.
%H Winston de Greef, <a href="/A354002/b354002.txt">Table of n, a(n) for n = 1..448</a>
%F E.g.f.: Sum_{k>=1} prime(k+1) * log(1 + x)^k / k!.
%F a(n) = Sum_{k=1..n} Stirling1(n,k) * prime(k+1).
%t nmax = 22; CoefficientList[Series[Sum[Prime[k + 1] Log[1 + x]^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
%t Table[Sum[StirlingS1[n, k] Prime[k + 1], {k, 1, n}], {n, 1, 22}]
%o (PARI) a(n) = sum(k=1, n, stirling(n,k,1) * prime(k+1)); \\ _Michel Marcus_, May 13 2022
%Y Cf. A065091, A307772, A307773, A353406, A354003.
%K sign
%O 1,1
%A _Ilya Gutkovskiy_, May 13 2022