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%I #8 Apr 27 2022 18:39:41
%S 1,3,14,79,521,3876,31935,287225,2791122,29066589,322292257,
%T 3784650052,46857941291,609360372095,8296220760974,117914344818807,
%U 1745211622467633,26838798853062516,428009369349905497,7065576909286562195,120545067517808693300,2122393931891338237325,38512344746420591905771
%N Exponential transform of odd primes.
%F E.g.f.: exp( Sum_{k>=1} prime(k+1) * x^k / k! ).
%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * prime(k+1) * a(n-k).
%p a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*
%p ithprime(j+1)*binomial(n-1, j-1), j=1..n))
%p end:
%p seq(a(n), n=0..22); # _Alois P. Heinz_, Apr 27 2022
%t nmax = 22; CoefficientList[Series[Exp[Sum[Prime[k + 1] x^k/k!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] Prime[k + 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 22}]
%Y Cf. A007446, A065091, A300632.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Apr 22 2022