A366729 -id:A366729 - cp's OEIS frontend

A367180 E.g.f. satisfies A(x) = 1 + (exp(x*A(x)^2) - 1)/A(x).

1, 1, 3, 19, 187, 2491, 41951, 855387, 20491395, 564179371, 17555839639, 609337562923, 23340215770235, 978038556122811, 44506423393073487, 2185725954288076987, 115224508775345033779, 6490005347933921581195, 388973650645651854960455

Offset: 0

Seiichi Manyama, Nov 08 2023

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..372

Cf. A000272, A367181.
Cf. A365438, A366729.
Cf. A349601.

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

a(n) = Sum_{k=0..n} (2*n-k)!/(2*n-2*k+1)! * Stirling2(n,k).

A367179 E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^3)/A(x)^2.

Original entry on oeis.org

1, 1, 1, -7, -74, 14, 10736, 124032, -1695672, -81281688, -528840024, 47385631512, 1540148366736, -12438137705904, -2292918626509536, -48210827445848832, 2456594159904115200, 177787615056364279296, 782103240212585461632

Offset: 0

Seiichi Manyama, Nov 08 2023

sign

Cf. A185221, A366729.

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

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

cp's OEIS Frontend

A367180 E.g.f. satisfies A(x) = 1 + (exp(x*A(x)^2) - 1)/A(x).

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