A346577
a(n) = (1/(3*n)) * Sum_{d|n} mu(n/d) * binomial(3*d,d).
Original entry on oeis.org
1, 2, 9, 40, 200, 1026, 5537, 30624, 173583, 1001400, 5864749, 34768296, 208267319, 1258574114, 7663720500, 46976003712, 289628805622, 1794932293950, 11175157356521, 69864074596000, 438403736543598, 2760351027094298, 17433869214973753, 110420300844952992
Offset: 1
Cf.
A001764,
A005809,
A008683,
A022553,
A060170,
A082936,
A346578,
A346579,
A346580,
A346581,
A346582.
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Table[(1/(3 n)) Sum[MoebiusMu[n/d] Binomial[3 d, d], {d, Divisors[n]}], {n, 24}]
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a(n) = sumdiv(n, d, moebius(n/d)*binomial(3*d,d))/(3*n); \\ Michel Marcus, Jul 24 2021
A346578
a(n) = (1/(4*n)) * Sum_{d|n} mu(n/d) * binomial(4*d,d).
Original entry on oeis.org
1, 3, 18, 112, 775, 5598, 42287, 328640, 2615085, 21191125, 174303162, 1451424960, 12211799223, 103655906781, 886568152950, 7633233227520, 66105170315083, 575445689879247, 5032380942945321, 44191451767056400, 389514699012969936, 3444925385161998518, 30561576846316109863
Offset: 1
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Table[(1/(4 n)) Sum[MoebiusMu[n/d] Binomial[4 d, d], {d, Divisors[n]}], {n, 23}]
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a(n) = sumdiv(n, d, moebius(n/d)*binomial(4*d,d))/(4*n); \\ Michel Marcus, Jul 24 2021
A346579
a(n) = (1/(5*n)) * Sum_{d|n} mu(n/d) * binomial(5*d,d).
Original entry on oeis.org
1, 4, 30, 240, 2125, 19776, 192129, 1922496, 19692504, 205444500, 2175519379, 23322637440, 252631900235, 2760767859780, 30400169155500, 336977763170048, 3757141504436392, 42107201575798248, 474084628585822412, 5359833703935374000, 60823006052351537106, 692556314455384443196
Offset: 1
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Table[(1/(5 n)) Sum[MoebiusMu[n/d] Binomial[5 d, d], {d, Divisors[n]}], {n, 22}]
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a(n) = sumdiv(n, d, moebius(n/d)*binomial(5*d,d))/(5*n); \\ Michel Marcus, Jul 24 2021
A346580
a(n) = (1/(6*n)) * Sum_{d|n} mu(n/d) * binomial(6*d,d).
Original entry on oeis.org
1, 5, 45, 440, 4750, 54081, 642341, 7861216, 98480286, 1256564750, 16273981757, 213378921432, 2826867619108, 37782552518473, 508840821825750, 6898459208449920, 94070535317459017, 1289430373107917718, 17755914760643605781, 245518560759177014000, 3407586451859019939012
Offset: 1
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Table[(1/(6 n)) Sum[MoebiusMu[n/d] Binomial[6 d, d], {d, Divisors[n]}], {n, 21}]
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a(n) = sumdiv(n, d, moebius(n/d)*binomial(6*d,d))/(6*n); \\ Michel Marcus, Jul 24 2021
A346582
a(n) = (1/(8*n)) * Sum_{d|n} mu(n/d) * binomial(8*d,d).
Original entry on oeis.org
1, 7, 84, 1120, 16450, 255612, 4141382, 69158272, 1182125043, 20581143150, 363704640475, 6506965023168, 117626432708863, 2145180354493274, 39421026305266125, 729242353100281344, 13568988503585900647, 253785064585174078869, 4768543107831461199896, 89970814565326816488000
Offset: 1
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Table[(1/(8 n)) Sum[MoebiusMu[n/d] Binomial[8 d, d], {d, Divisors[n]}], {n, 20}]
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a(n) = sumdiv(n, d, moebius(n/d)*binomial(8*d,d))/(8*n); \\ Michel Marcus, Jul 24 2021
Showing 1-5 of 5 results.
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