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%I #16 Sep 08 2022 08:45:13
%S 1,2,4,8,15,31,62,126,283,539,1177,2459,4969,10781,22297,45116,95759,
%T 201615,400755,830859,1741455,3505627,7099561,14607199,30112789,
%U 60176505,121626832,247652036,504389269,1010060135,2030792857,4102303316,8289676399,16659582365
%N a(n) = Sum_{k=1..n} min(k!, binomial(n,k)).
%C Upper bound on A088532(n).
%C The number of patterns of length k in a permutation of length n is bounded above by k! and binomial(n,k). The total number of patterns in a permutation of length n is therefore bounded above by the sum of the smaller of these two upper bounds.
%F a(n) ~ 2^n. - _Vaclav Kotesovec_, Aug 03 2015
%t Table[Sum[Min[k!, Binomial[n, k]], {k, 1, n}], {n, 1, 40}]
%o (PARI) a(n) = sum(k=1, n, min(k!, binomial(n, k))); \\ _Michel Marcus_, Nov 14 2019
%o (Magma) [&+[Min(Factorial(k),Binomial(n,k)):k in [1..n]]:n in [1..34]]; // _Marius A. Burtea_, Nov 14 2019
%Y Cf. A088532.
%K easy,nonn
%O 1,2
%A _Rob Pratt_, Apr 10 2004