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A254593 a(n) = (3/n^3) * Sum_{d|n} (-1)^(n+d)*moebius(n/d)*binomial(2*d,d). 4
6, 3, 2, 3, 6, 13, 30, 75, 200, 555, 1590, 4693, 14202, 43863, 137882, 440235, 1424958, 4668304, 15459366, 51692379, 174362770, 592815459, 2030105382, 6998177293, 24270836436, 84646997613, 296744311172, 1045283877639, 3698462401026, 13140509079977, 46869358523238, 167781751129899 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1650

R. R. Aidagulov, M. A. Alekseyev. On p-adic approximation of sums of binomial coefficients. Journal of Mathematical Sciences 233:5 (2018), 626-634. doi:10.1007/s10958-018-3948-0 arXiv:1602.02632

M. Kontsevich, R. Stanley, O. Gorodetsky, et al. A congruence involving binomial coefficients, Mathoverflow, 2015.

FORMULA

a(n) = 6*A131868(n)/n.

For n == 0, 1, or 3 (mod 4), a(n) = A268592(n)/2; for n == 2 (mod 4), a(n) = A268592(n)/2 + A268592(n/2)/8.

MATHEMATICA

a[n_] := 3/n^3 DivisorSum[n, (-1)^(n+#) MoebiusMu[n/#] Binomial[2#, #]&]; Array[a, 40] (* Jean-Fran├žois Alcover, Dec 18 2015 *)

PROG

(PARI) { a(n) = sumdiv(n, d, (-1)^(n+d)*moebius(n/d)*binomial(2*d, d))*3/n^3 }

CROSSREFS

Sequence in context: A226579 A129203 A083946 * A153607 A010494 A078333

Adjacent sequences:  A254590 A254591 A254592 * A254594 A254595 A254596

KEYWORD

nonn

AUTHOR

Max Alekseyev, Feb 01 2015

STATUS

approved

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Last modified November 13 10:50 EST 2019. Contains 329093 sequences. (Running on oeis4.)