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A121774
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Number of n-bead necklaces with n+1 colors, divided by (n+1), for n>0, with a(0)=1.
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2
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1, 1, 2, 6, 33, 260, 2812, 37450, 597965, 11111134, 235796238, 5628851294, 149346730841, 4361070182716, 139013934267864, 4803839602537336, 178901440745010273, 7143501829211426576, 304465936544543927890
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..18.
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FORMULA
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a(n) = (1/n)*Sum_{d|n} phi(n/d)*(n+1)^(d-1), for n>0, with a(0)=1.
a(n) = Sum_{k=0..[n/2]} A152290(n, n*k), where A152290 is a triangle of coefficients in a q-analog of the LambertW function. - Paul D. Hanna, Jul 18 2013
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PROG
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(PARI) a(n)=if(n==0, 1, (1/n)*sumdiv(n, d, eulerphi(n/d)*(n+1)^(d-1)))
(PARI) /* a(n) = Sum_{k=0..[n/2]} A152290(n, n*k): */
{A152290(n, k)=local(e_q=1+sum(j=1, n, x^j/prod(i=1, j, (q^i-1)/(q-1))), LW_q=serreverse(x/e_q+x^2*O(x^n))/x); polcoeff(polcoeff(LW_q+x*O(x^n), n, x)*prod(i=1, n, (q^i-1)/(q-1))+q*O(q^k), k, q)}
{a(n)=sum(k=0, n\2, A152290(n, n*k))}
for(n=0, 20, print1(a(n), ", ")) \\ Paul D. Hanna, Jul 18 2013
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CROSSREFS
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Cf. A121773, A056665, A152290.
Sequence in context: A127114 A138909 A138983 * A209238 A053042 A174432
Adjacent sequences: A121771 A121772 A121773 * A121775 A121776 A121777
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Aug 20 2006
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STATUS
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approved
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