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A097936 Total number of parts in all compositions of n into distinct odd parts. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A050338 A301598

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

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Last modified January 23 01:15 EST 2020. Contains 331166 sequences. (Running on oeis4.)