A367179 -id:A367179 - cp's OEIS frontend

A367181 E.g.f. satisfies A(x) = 1 + (exp(x*A(x)^3) - 1)/A(x)^2.

1, 1, 3, 22, 261, 4186, 85035, 2096242, 60793257, 2028053146, 76512294567, 3221179205410, 149713378082301, 7614267616582810, 420634056602820099, 25081994054279063506, 1605673188973569254481, 109838361160586478627226, 7995918540574019507985471

Offset: 0

Seiichi Manyama, Nov 08 2023

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..362

Cf. A000272, A367180.

Cf. A365546, A367179.

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

a(n) = Sum_{k=0..n} (3*n-2*k)!/(3*n-3*k+1)! * Stirling2(n,k).

A366729 E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^2)/A(x).

Original entry on oeis.org

1, 1, 1, -4, -36, 14, 3100, 22112, -374640, -9520320, 9674808, 4085208192, 55207595520, -1640647901088, -69445046214336, 103240707929088, 71686341699216384, 1439635203885275136, -60449514895261440000, -3608840044036879934976

Offset: 0

Seiichi Manyama, Nov 08 2023

sign

Cf. A185221, A367179.

Cf. A365438, A367180.

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

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

cp's OEIS Frontend

A367181 E.g.f. satisfies A(x) = 1 + (exp(x*A(x)^3) - 1)/A(x)^2.

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