A258797 a(n) = [x^n] Product_{k=1..n} (1+x^k)^2 / x^k.

1, 1, 2, 6, 16, 51, 166, 554, 1896, 6595, 23212, 82582, 296393, 1071738, 3900696, 14278074, 52526972, 194108087, 720197524, 2681854490, 10019539112, 37545876368, 141080872362, 531457445806, 2006678785762, 7593123695669, 28789152013570, 109356019134584

Offset

0,3

Comments

a(n) is half the number of subsets of {-n..n} whose sum is n. - Ilya Gutkovskiy, Jul 09 2025

Links

Alois P. Heinz, Table of n, a(n) for n = 0..555

Formula

a(n) ~ sqrt(3) * 4^n / (sqrt(Pi) * n^(3/2)).

Maple

b:= proc(n, s) option remember; `if`(n*(n+1)/2<s, 0, `if`(n=0, 1,
      add(`if`(j=0, 2, 1)*b(n-1, abs(s+j*n)), j=-1..1)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..27);  # Alois P. Heinz, Jul 14 2025

Mathematica

Table[SeriesCoefficient[Product[(1+x^k)^2/x^k, {k, 1, n}], {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[Product[1+x^k, {k, 1, n}]^2, {x, 0, n*(n+3)/2}], {n, 0, 30}]

Crossrefs

Cf. A022567, A047653, A258798, A258799.

Sequence in context: A317094 A382315 A339844 * A360232 A214983 A367389

Adjacent sequences: A258794 A258795 A258796 * A258798 A258799 A258800

Keyword

nonn

Author

Vaclav Kotesovec, Jun 10 2015

Status

approved