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

Links

Table of n, a(n) for n=0..27.

Formula

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

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. A258798, A258799.

Sequence in context: A100664 A317094 A339844 * A360232 A214983 A367389

Adjacent sequences: A258794 A258795 A258796 * A258798 A258799 A258800

Keyword

nonn

Author

Vaclav Kotesovec, Jun 10 2015

Status

approved