A182103 Integral of exp(-x)*Phi_n(x) from 0 to infinity, Phi_n the n-th cyclotomic polynomial.

0, 2, 4, 3, 34, 2, 874, 25, 727, 20, 4037914, 23, 522956314, 620, 35382, 40321, 22324392524314, 715, 6780385526348314, 39623, 439408062, 3301820, 1177652997443428940314, 40297, 2432903315854636921, 442386620, 6402373706090881, 475412423

Offset: 1

Author

Jair Taylor, Apr 11 2012

Keywords

• nonn

Comments

Appears to be all positive integers for n>1, suggesting the possibility of a combinatorial interpretation.

Links

• Jair Taylor, Table of n, a(n) for n = 1..497

Crossrefs

Agrees with A003422(p) for p prime.

Programs

Mathematica

Table[Integrate[Cyclotomic[n, x]/Exp[x], {x, 0, Infinity}], {n, 1, 20}] (* Vaclav Kotesovec, Mar 01 2020 *)

Sage

for n in range(1, 40):
  print(integral(e^(-x)*cyclotomic_polynomial(n),x,0,infinity))