A102623 Number of compositions into a prime number of distinct parts.

0, 0, 2, 2, 4, 10, 12, 18, 26, 32, 40, 52, 60, 72, 206, 218, 352, 490, 744, 1002, 1382, 1760, 2380, 3004, 3864, 4728, 5954, 12218, 13804, 20554, 27660, 39930, 52682, 75632, 99184, 132940, 172332, 227088, 287606, 373562, 465280, 587602, 725880, 899802, 1094846

Offset: 1

Author

Vladeta Jovovic, Jan 31 2005

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A085756, A052467, A038499.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, [1],
      `if`(n>i*(i+1)/2, [], zip((x, y)->x+y, b(n, i-1),
      `if`(i>n, [], [0, b(n-i, i-1)[]]), 0)))
    end:
a:= proc(n) local l; l:= b(n$2);
      add(`if`(isprime(i), l[i+1]*i!, 0), i=2..nops(l)-1)
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, Nov 20 2012

Mathematica

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 *)

Formula

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).

Extensions

More terms from Robert G. Wilson v, Feb 04 2005