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A102623 Number of compositions into a prime number of distinct parts. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 18 16:00 EDT 2019. Contains 321292 sequences. (Running on oeis4.)