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%I #17 Oct 03 2021 10:19:27
%S 1,2,2,6,2,234,2,331842,46658,24883200258,2,139314179589392898,2,
%T 82606411253903523840004098,619173642242176782338,
%U 6984964247141514123665660725036072962,2,109110688415571335888754861121236891599318185050114,2
%N a(n) = Sum_{d|n} (d!)^(n-d).
%H Seiichi Manyama, <a href="/A348146/b348146.txt">Table of n, a(n) for n = 1..61</a>
%F a(p) = 2 for primes p.
%F G.f.: Sum_{k>=1} x^k/(1 - (k! * x)^k). - _Seiichi Manyama_, Oct 03 2021
%t Table[Sum[(i!)^(n - i) (1 - Ceiling[n/i] + Floor[n/i]), {i, n}], {n, 20}]
%o (PARI) a(n) = sumdiv(n, d, d!^(n-d)); \\ _Seiichi Manyama_, Oct 03 2021
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(k!*x)^k))) \\ _Seiichi Manyama_, Oct 03 2021
%Y Cf. A062363, A342628, A345465, A346196.
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, Oct 02 2021
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