A105200 Number of compositions of n such that the least part occurs with odd multiplicity.

1, 1, 4, 3, 13, 16, 41, 64, 154, 261, 560, 1049, 2176, 4169, 8474, 16614, 33477, 66178, 132776, 263969, 528519, 1053483, 2107772, 4207680, 8415341, 16812773, 33622527, 67203682, 134391649, 268686218, 537318189, 1074403625, 2148636672, 4296709932, 8592918851

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..600

Formula

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).

a(n) ~ 2^(n-2). - Vaclav Kotesovec, Sep 10 2014

Maple

b:= proc(n, i, p) option remember; `if`(i<1, 0, add(
      `if`(n=i*j, `if`(irem(j, 2)=1, (p+j)!/j!, 0),
       b(n-i*j, i-1, p+j)/j!), j=0..n/i))
    end:
a:= proc(n) option remember; b(n$2, 0) end:
seq(a(n), n=1..45);  # Alois P. Heinz, May 13 2014

Mathematica

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 *)

Crossrefs

Cf. A096375.

Sequence in context: A120340 A082018 A056477 * A088933 A019136 A298057

Adjacent sequences: A105197 A105198 A105199 * A105201 A105202 A105203

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 12 2005

Extensions

More terms from Robert G. Wilson v, Apr 12 2005

Status

approved