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

1,4

Links

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

Formula

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

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 *)

Crossrefs

Cf. A097910, A079499, A032021.

Sequence in context: A322819 A089655 A322820 * A277027 A354969 A050338

Adjacent sequences: A097933 A097934 A097935 * A097937 A097938 A097939

Keyword

easy,nonn

Author

Vladeta Jovovic, Sep 05 2004

Extensions

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

Status

approved