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

1,3

Links

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

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).

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 *)

Crossrefs

Cf. A085756, A052467, A038499.

Sequence in context: A199400 A056919 A052175 * A216695 A320069 A002082

Adjacent sequences: A102620 A102621 A102622 * A102624 A102625 A102626

Keyword

easy,nonn

Author

Vladeta Jovovic, Jan 31 2005

Extensions

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

Status

approved