A377349 -id:A377349 - cp's OEIS frontend

A377350 E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^3)/A(x)^3.

1, 1, 1, 11, 108, 1584, 29808, 674988, 18091944, 557844408, 19468760904, 758698622472, 32653135227936, 1538316755200224, 78737559447563136, 4350956519444451840, 258163046132873143680, 16370486288763937324416, 1104824513292622360789248, 79068747951669626322531840

Offset: 0

Seiichi Manyama, Oct 26 2024

nonn

Cf. A365546, A367139, A367152, A377323, A377327.

Cf. A377325, A377349.

a(n) = sum(k=0, (3*n+1)\4, (3*n-3*k)!/(3*n-4*k+1)!*abs(stirling(n, k, 1)));

a(n) = Sum_{k=0..floor((3*n+1)/4)} (3*n-3*k)!/(3*n-4*k+1)! * |Stirling1(n,k)|.

A377358 E.g.f. satisfies A(x) = ( 1 - log(1 - x*A(x))/A(x) )^2.

Original entry on oeis.org

1, 2, 4, 22, 194, 2268, 34272, 624804, 13432120, 332078160, 9286572624, 289821031344, 9985648515504, 376489542984384, 15418392593403360, 681562973789926560, 32345053760113660800, 1640243700728870131200, 88516191520113318169344, 5064936155664187593030912

Offset: 0

Seiichi Manyama, Oct 26 2024

nonn

Cf. A377325, A377359.

Cf. A377349.

a(n) = 2*sum(k=0, (2*n+2)\3, (2*n-2*k+1)!/(2*n-3*k+2)!*abs(stirling(n, k, 1)));

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377349.

a(n) = 2 * Sum_{k=0..floor((2*n+2)/3)} (2*n-2*k+1)!/(2*n-3*k+2)! * |Stirling1(n,k)|.

cp's OEIS Frontend

A377350 E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^3)/A(x)^3.

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