A102623 - OEIS

%I #18 Sep 24 2015 18:45:35

%S 0,0,2,2,4,10,12,18,26,32,40,52,60,72,206,218,352,490,744,1002,1382,

%T 1760,2380,3004,3864,4728,5954,12218,13804,20554,27660,39930,52682,

%U 75632,99184,132940,172332,227088,287606,373562,465280,587602,725880,899802,1094846

%N Number of compositions into a prime number of distinct parts.

%H Alois P. Heinz, <a href="/A102623/b102623.txt">Table of n, a(n) for n = 1..5000</a>

%F G.f.: Sum(prime(k)!*x^(1/2*prime(k)^2+1/2*prime(k))/Product(1-x^j, j = 1 .. prime(k)), k = 1 .. infinity).

%p b:= proc(n, i) option remember; `if`(n=0, [1],

%p       `if`(n>i*(i+1)/2, [], zip((x, y)->x+y, b(n, i-1),

%p       `if`(i>n, [], [0, b(n-i, i-1)[]]), 0)))

%p     end:

%p a:= proc(n) local l; l:= b(n$2);

%p       add(`if`(isprime(i), l[i+1]*i!, 0), i=2..nops(l)-1)

%p     end:

%p seq(a(n), n=1..50);  # _Alois P. Heinz_, Nov 20 2012

%t CoefficientList[ Series[ Sum[ Prime[k]!* x^(Prime[k]^2/2 + Prime[k]/2)/Product[1 - x^j, {j, Prime[k]}], {k, 44}], {x, 0, 44}], x] (* _Robert G. Wilson v_, Feb 04 2005 *)

%Y Cf. A085756, A052467, A038499.

%K easy,nonn

%O 1,3

%A _Vladeta Jovovic_, Jan 31 2005

%E More terms from _Robert G. Wilson v_, Feb 04 2005