A366459 -id:A366459 - cp's OEIS frontend

A366546 Expansion of e.g.f. -log(1 - x^3 * exp(x)).

0, 0, 0, 6, 24, 60, 480, 5250, 40656, 363384, 4839120, 65198430, 859543080, 13311494196, 233478687624, 4190929145130, 79746180437280, 1667320408619760, 36965002127643936, 854734007793179574, 20962277675893792440, 544839141515795731500

Offset: 0

Seiichi Manyama, Dec 14 2023

nonn

Cf. A009444, A366459.

Cf. A292889, A346754, A358081.

a(n) = n!*sum(k=1, n\3, k^(n-3*k-1)/(n-3*k)!);

a(n) = n! * Sum_{k=1..floor(n/3)} k^(n-3*k-1)/(n-3*k)!.

A366564 Expansion of e.g.f. -log(1 - x^2 * (exp(x) - 1)).

Original entry on oeis.org

0, 0, 0, 6, 12, 20, 390, 2562, 11816, 166392, 1970730, 17131070, 241009692, 3861669396, 51411143966, 828234487290, 15865154629200, 283329069136112, 5431892804244306, 119420738547382134, 2628980439169097540, 59707303735169923980, 1488953374718002643142

Offset: 0

Seiichi Manyama, Dec 15 2023

nonn

Cf. A052858, A366751.

Cf. A366459, A368173.

a(n) = n!*sum(k=1, n\3, (k-1)!*stirling(n-2*k, k, 2)/(n-2*k)!);

a(n) = n! * Sum_{k=1..floor(n/3)} (k-1)! * Stirling2(n-2*k,k)/(n-2*k)!.

cp's OEIS Frontend

A366546 Expansion of e.g.f. -log(1 - x^3 * exp(x)).

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