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A318433
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Number of n-element subsets of [5n] whose elements sum to a multiple of n.
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4
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1, 5, 20, 155, 1220, 10630, 98900, 960650, 9613700, 98462675, 1027222520, 10877596900, 116613287300, 1263159501180, 13803839298920, 152000845788280, 1684888825463940, 18785707522181965, 210536007879090140, 2370423142929112065, 26799168520704093720
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..20.
Marko Riedel et al., Number of n-element subsets divisible by n
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FORMULA
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a(n) = (-1)^n * (1/n) * Sum_{d|n} C(5d,d)*(-1)^d*phi(n/d) for n>0, a(0)=1.
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MAPLE
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with(numtheory); a := n -> `if`(n=0, 1, (-1)^n * 1/n * add(binomial(5*d, d)*(-1)^d*phi(n/d), d in divisors(n)));
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PROG
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(PARI) a(n) = if (n, (-1)^n * (1/n) * sumdiv(n, d, binomial(5*d, d)*(-1)^d*eulerphi(n/d)), 1); \\ Michel Marcus, Aug 27 2018
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CROSSREFS
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Cf. A169888, A318431, A318432.
Column k=5 of A304482.
Sequence in context: A061964 A133667 A354848 * A205338 A197857 A197741
Adjacent sequences: A318430 A318431 A318432 * A318434 A318435 A318436
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KEYWORD
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nonn
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AUTHOR
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Marko Riedel, Aug 26 2018
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STATUS
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approved
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