%I #7 Jul 25 2021 02:41:21

%S 1,5,45,440,4750,54081,642341,7861216,98480286,1256564750,16273981757,

%T 213378921432,2826867619108,37782552518473,508840821825750,

%U 6898459208449920,94070535317459017,1289430373107917718,17755914760643605781,245518560759177014000,3407586451859019939012

%N a(n) = (1/(6*n)) * Sum_{d|n} mu(n/d) * binomial(6*d,d).

%C Inverse Euler transform of A002295.

%C Moebius transform of A261499.

%t Table[(1/(6 n)) Sum[MoebiusMu[n/d] Binomial[6 d, d], {d, Divisors[n]}], {n, 21}]

%o (PARI) a(n) = sumdiv(n, d, moebius(n/d)*binomial(6*d,d))/(6*n); \\ _Michel Marcus_, Jul 24 2021

%Y Cf. A002295, A004355, A008683, A022553, A261499, A346577, A346578, A346579, A346581, A346582.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Jul 24 2021