A097936 Total number of parts in all compositions of n into distinct odd parts.

1, 0, 1, 4, 1, 4, 1, 8, 19, 8, 19, 12, 37, 12, 55, 112, 73, 112, 91, 212, 127, 308, 145, 504, 781, 600, 817, 892, 1453, 1084, 2089, 1472, 3343, 1760, 4579, 6564, 6433, 6948, 8287, 11944, 11341, 16744, 14395, 26156, 18667, 35468, 22921, 53712, 64273, 67440

Offset: 1

Author

Vladeta Jovovic, Sep 05 2004

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A097910, A079499, A032021.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1,
      `if`(n>(i+1)^2/4, [][], zip((x, y)->x+y, [b(n, i-2)],
      `if`(i>n, [], [0, b(n-i, i-2)]), 0)[]))
    end:
a:= proc(n) option remember; local l; l:=[b(n, n-1+irem(n,2))];
      add(i*l[i+1]*i!, i=1..nops(l)-1)
    end:
seq (a(n), n=1..60);  # Alois P. Heinz, Nov 20 2012

Mathematica

Drop[ CoefficientList[ Series[Sum[k*k!*x^k^2/Product[1 - x^(2j), {j, 1, k}], {k, 1, 55}], {x, 0, 50}], x], 1] (* Robert G. Wilson v, Sep 08 2004 *)

Formula

Sum_{k>0} (k*k!*x^(k^2)/Product_{j=1..k} (1-x^(2*j))).

Extensions

More terms from Robert G. Wilson v, Sep 08 2004