A182103 - OEIS

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

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OFFSET

1,2

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

MATHEMATICA

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

PROG

(Sage)

for n in range(1, 40):

print(integral(e^(-x)*cyclotomic_polynomial(n), x, 0, infinity))

CROSSREFS

Agrees with A003422(p) for p prime.

Sequence in context: A229213 A356063 A071970 * A303053 A163089 A370635

Adjacent sequences: A182100 A182101 A182102 * A182104 A182105 A182106

KEYWORD

nonn

AUTHOR

Jair Taylor, Apr 11 2012

STATUS

approved