A297326 a(n) = [x^n] Product_{k>=1} 1/(1 + k*x^k)^n.

1, -1, -1, -1, 27, -76, 95, -295, 2035, -8119, 22714, -66793, 254223, -988651, 3444055, -11402626, 39248691, -141740051, 511583207, -1798826901, 6256648862, -22054706773, 78889160635, -281698897727, 996551999479, -3520566280801, 12522382445455, -44731559517301

Offset: 0

Author

Ilya Gutkovskiy, Dec 28 2017

Keywords

• sign

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Main diagonal of A297325.

Cf. A297322, A297324, A297329.

Programs

Maple

f:= proc(n) local k;
coeff(series(mul(1/(1+k*x^k)^n,k=1..n),x,n+1),x,n);
end proc:
map(f, [$0..30]); # Robert Israel, Dec 28 2017

Mathematica

Table[SeriesCoefficient[Product[1/(1 + k x^k)^n, {k, 1, n}], {x, 0, n}], {n, 0, 27}]

Formula

a(n) = A297325(n,n).