The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A318433 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A318433

Number of n-element subsets of [5n] whose elements sum to a multiple of n.
(history; published version)

#18 by Alois P. Heinz at Tue Aug 28 19:27:25 EDT 2018

STATUS

editing

approved

#17 by Alois P. Heinz at Tue Aug 28 19:27:22 EDT 2018

CROSSREFS

Column k=5 of A304482.

STATUS

approved

editing

#16 by Alois P. Heinz at Mon Aug 27 14:45:59 EDT 2018

STATUS

editing

approved

#15 by Alois P. Heinz at Mon Aug 27 14:45:58 EDT 2018

LINKS

Marko Riedel et al., <a href="https://math.stackexchange.com/questions/2894653/">Number of n-element subsets divisible by n</a>

FORMULA

a(n) = (-1)^n * (1/n) * Sum_{d|n} C(5d,d)*(-1)^d*phi(n/d) for n>0, a(0)=1.

STATUS

approved

editing

#14 by Alois P. Heinz at Mon Aug 27 14:44:32 EDT 2018

STATUS

editing

approved

#13 by Alois P. Heinz at Mon Aug 27 14:44:29 EDT 2018

MAPLE

with(numtheory); A a := n -> `if`(n=0, 1, (-1)^n * 1/n * add(binomial(5*d, d)*(-1)^d*phi(n/d), d in divisors(n)));

STATUS

proposed

editing

#12 by Michel Marcus at Mon Aug 27 02:50:30 EDT 2018

STATUS

editing

proposed

#11 by Michel Marcus at Mon Aug 27 02:50:26 EDT 2018

PROG

(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

STATUS

proposed

editing

#10 by Joerg Arndt at Mon Aug 27 02:01:32 EDT 2018

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editing

proposed

#9 by Alois P. Heinz at Sun Aug 26 17:28:16 EDT 2018

DATA

1, 5, 20, 155, 1220, 10630, 98900, 960650, 9613700, 98462675, 1027222520, 10877596900, 116613287300, 1263159501180, 13803839298920, 152000845788280, 1684888825463940, 18785707522181965, 210536007879090140, 2370423142929112065, 26799168520704093720

OFFSET

1,1

0,2

STATUS

proposed

editing