OFFSET
0,5
COMMENTS
a(n) = Sum_{k>=0} k*A264399(n,k).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: g(x) = (Sum_{j>=1} (x^(2j)/(1+x^j))) / Product_{k>=1} (1-x^k).
EXAMPLE
a(6) = 6 because we have [6], [5,1], [4,2], [4,1*,1], [3*,3], [3,2,1], [3,1,1,1], [2,2,2], [2*,2,1*,1], [2,1*,1,1,1], and [1*,1,1,1,1,1] (the 6 parts with even multiplicities are marked).
MAPLE
g := (sum(x^(2*j)/(1+x^j), j = 1 .. 100))/(product(1-x^j, j = 1 .. 100)): gser := series(g, x = 0, 70): seq(coeff(gser, x, n), n = 0 .. 60);
MATHEMATICA
Needs["Combinatorica`"]; Table[Count[Last /@ Flatten[Tally /@ Combinatorica`Partitions@ n, 1], k_ /; EvenQ@ k], {n, 0, 50}] (* Michael De Vlieger, Nov 21 2015 *)
PROG
(PARI) { my(n=50); Vec(sum(k=1, n, x^(2*k)/(1+x^k) + O(x*x^n)) / prod(k=1, n, 1-x^k + O(x*x^n)), -(n+1)) } \\ Andrew Howroyd, Dec 22 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Nov 21 2015
STATUS
approved