A331926 Number of compositions (ordered partitions) of n into distinct prime parts (counting 1 as a prime).

1, 1, 1, 3, 2, 3, 8, 3, 10, 8, 14, 31, 10, 33, 16, 38, 40, 61, 138, 69, 48, 98, 190, 121, 308, 128, 340, 270, 472, 991, 572, 885, 534, 446, 888, 1872, 914, 1927, 1084, 2300, 2058, 4303, 6508, 3759, 2246, 4856, 8238, 6889, 12630, 6368, 8708

Offset: 0

Author

Ilya Gutkovskiy, Feb 01 2020

Keywords

• nonn

Examples

			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].
		

Links

• Index entries for sequences related to compositions

Crossrefs

Cf. A008578, A023360, A034891, A036497, A219107, A280917.

Programs

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