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A353406 Stirling transform of odd primes.

%I A353406 #9 May 13 2022 12:49:12
%S A353406 3,8,25,91,376,1715,8471,44838,252903,1514213,9590874,64056173,
%T A353406 449804453,3312346950,25521479277,205300781275,1720450321356,
%U A353406 14986361037495,135393159641569,1266006310597506,12228936468908781,121823473948915769,1249794986354577736
%N A353406 Stirling transform of odd primes.
%F A353406 E.g.f.: Sum_{k>=1} prime(k+1) * (exp(x) - 1)^k / k!.
%F A353406 a(n) = Sum_{k=1..n} Stirling2(n,k) * prime(k+1).
%p A353406 b:= proc(n, m) option remember;
%p A353406      `if`(n=0, ithprime(m+1), m*b(n-1, m)+b(n-1, m+1))
%p A353406     end:
%p A353406 a:= n-> b(n-1, 1):
%p A353406 seq(a(n), n=1..23);  # _Alois P. Heinz_, May 13 2022
%t A353406 nmax = 23; CoefficientList[Series[Sum[Prime[k + 1] (Exp[x] - 1)^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
%t A353406 Table[Sum[StirlingS2[n, k] Prime[k + 1], {k, 1, n}], {n, 1, 23}]
%Y A353406 Cf. A065091, A307771, A351681.
%K A353406 nonn
%O A353406 1,1
%A A353406 _Ilya Gutkovskiy_, May 07 2022