A105200 - OEIS

%I #11 Sep 10 2014 11:16:26

%S 1,1,4,3,13,16,41,64,154,261,560,1049,2176,4169,8474,16614,33477,

%T 66178,132776,263969,528519,1053483,2107772,4207680,8415341,16812773,

%U 33622527,67203682,134391649,268686218,537318189,1074403625,2148636672,4296709932,8592918851

%N Number of compositions of n such that the least part occurs with odd multiplicity.

%H Alois P. Heinz, <a href="/A105200/b105200.txt">Table of n, a(n) for n = 1..600</a>

%F G.f.: Sum(Sum(binomial(k, 2*l-1)*x^(2*k-2*l+1)/((1-x)^(k-2*l+1)*(1-x^k)), l=1..floor((k+1)/2)), k=1..infinity).

%F a(n) ~ 2^(n-2). - _Vaclav Kotesovec_, Sep 10 2014

%p b:= proc(n, i, p) option remember; `if`(i<1, 0, add(

%p       `if`(n=i*j, `if`(irem(j, 2)=1, (p+j)!/j!, 0),

%p        b(n-i*j, i-1, p+j)/j!), j=0..n/i))

%p     end:

%p a:= proc(n) option remember; b(n$2, 0) end:

%p seq(a(n), n=1..45);  # _Alois P. Heinz_, May 13 2014

%t Rest[ CoefficientList[ Series[ Sum[ Binomial[k, 2l - 1] x^(2k - 2l + 1)/((1 - x)^(k - 2*l + 1)(1 - x^k)), {k, 34}, {l, Floor[(k + 1)/2]}], {x, 0, 34}], x]] (* _Robert G. Wilson v_, Apr 12 2005 *)

%Y Cf. A096375.

%K easy,nonn

%O 1,3

%A _Vladeta Jovovic_, Apr 12 2005

%E More terms from _Robert G. Wilson v_, Apr 12 2005