

A242911


Half the number of compositions of n into exactly two different parts with equal multiplicities.


1



1, 1, 2, 5, 3, 6, 14, 10, 5, 56, 6, 15, 153, 51, 8, 502, 9, 217, 1756, 25, 11, 7023, 264, 30, 24363, 1852, 14, 93629, 15, 6576, 352782, 40, 3827, 1377543, 18, 45, 5200379, 105812, 20, 20063228, 21, 352942, 77607976, 55, 23, 301906830, 5172, 185320, 1166803215
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OFFSET

3,3


LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..1000


FORMULA

a(n) = 1/2 * Sum_{dn} floor(d1/2) * C(2*n/d,n/d).
a(p) = (p1)/2 for odd prime p.
a(n) = 1/2 * (A131661(n)A242900(n)).


EXAMPLE

a(6) = 5 because there are 10 compositions of 6 into exactly two different parts with equal multiplicities: [1,5], [5,1], [2,4], [4,2], [1,1,2,2], [1,2,1,2], [1,2,2,1], [2,1,1,2], [2,1,2,1], [2,2,1,1].


MAPLE

a:= n> add(iquo(d1, 2)*binomial(2*n/d, n/d),
d=numtheory[divisors](n))/2:
seq(a(n), n=3..60);


MATHEMATICA

a[n_] := DivisorSum[n, Quotient[#1, 2]*Binomial[2n/#, n/#]&]/2; Table[ a[n], {n, 3, 60}] (* JeanFrançois Alcover, Feb 28 2017, translated from Maple *)


CROSSREFS

Sequence in context: A194280 A163362 A243061 * A112486 A253924 A141410
Adjacent sequences: A242908 A242909 A242910 * A242912 A242913 A242914


KEYWORD

nonn


AUTHOR

Alois P. Heinz, May 26 2014


STATUS

approved



