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%I #6 Feb 01 2020 22:36:57
%S 1,1,1,3,2,3,8,3,10,8,14,31,10,33,16,38,40,61,138,69,48,98,190,121,
%T 308,128,340,270,472,991,572,885,534,446,888,1872,914,1927,1084,2300,
%U 2058,4303,6508,3759,2246,4856,8238,6889,12630,6368,8708
%N Number of compositions (ordered partitions) of n into distinct prime parts (counting 1 as a prime).
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%e a(6) = 8 because we have [5, 1], [3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 1, 3], [1, 5], [1, 3, 2] and [1, 2, 3].
%o (PARI) a(n)={subst(serlaplace(y^0*polcoef(prod(k=1, n, 1 + if(k==1 || isprime(k), y*x^k) + O(x*x^n)), n)), y, 1)} \\ _Andrew Howroyd_, Feb 01 2020
%Y Cf. A008578, A023360, A034891, A036497, A219107, A280917.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Feb 01 2020
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