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A182103
Integral of exp(-x)*Phi_n(x) from 0 to infinity, Phi_n the n-th cyclotomic polynomial
1
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
1,2
COMMENTS
Appears to be all positive integers for n>1, suggesting the possibility of a combinatorial interpretation.
LINKS
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
KEYWORD
nonn
AUTHOR
Jair Taylor, Apr 11 2012
STATUS
approved