A105201 Number of compositions of n such that the least part occurs with even multiplicity.

0, 1, 0, 5, 3, 16, 23, 64, 102, 251, 464, 999, 1920, 4023, 7910, 16154, 32059, 64894, 129368, 260319, 520057, 1043669, 2086532, 4180928, 8361875, 16741659, 33486337, 67014046, 134043807, 268184694, 536423635, 1073080023, 2146330624

Offset

1,4

Links

Table of n, a(n) for n=1..33.

Formula

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

Mathematica

CoefficientList[ Series[ Sum[ Binomial[k, 2l] x^(2k - 2l)/((1 - x)^(k - 2*l)(1 - x^k)), {k, 34}, {l, Floor[k/2]}], {x, 0, 34}], x] (* Robert G. Wilson v, Apr 12 2005 *)

Crossrefs

Cf. A096374.

Sequence in context: A213571 A185880 A292243 * A184537 A187809 A092893

Adjacent sequences: A105198 A105199 A105200 * A105202 A105203 A105204

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 12 2005

Extensions

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

Status

approved