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A105200 Number of compositions of n such that the least part occurs with odd multiplicity. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A140884

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

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Last modified December 3 21:14 EST 2016. Contains 278745 sequences.