A377692 -id:A377692 - cp's OEIS frontend

A377693 E.g.f. satisfies A(x) = (1 - log(1 - x) * A(x))^3.

1, 3, 27, 408, 8814, 249702, 8789946, 370639896, 18233312640, 1025931258264, 65016004033944, 4583861319427200, 355955157532869552, 30192068409536580336, 2777615578746538933392, 275502517287785484635520, 29308962522270448504338048, 3329136621436554585165282048

Offset: 0

Seiichi Manyama, Nov 04 2024

nonn

Cf. A007840, A377692.

Cf. A367158, A377446.

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A367158.

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

A377716 E.g.f. satisfies A(x) = (1 + (exp(x) - 1) * A(x))^2.

Original entry on oeis.org

1, 2, 12, 116, 1584, 28172, 619872, 16289996, 498428544, 17417438252, 684759380832, 29925135793676, 1439467532867904, 75591768584407532, 4303733247493423392, 264082643528395550156, 17375242687235713361664, 1220318925238762558532012, 91128522664443184593699552

Offset: 0

Seiichi Manyama, Nov 04 2024

Cf. A000670, A377717.

Cf. A052895, A377692.

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

E.g.f.: 4/(1 + sqrt(5 - 4*exp(x)))^2.
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052895.
a(n) = 2 * Sum_{k=0..n} (2*k+1)!/(k+2)! * Stirling2(n,k).
a(n) ~ 2^(5/2) * sqrt(5) * n^(n-1) / (exp(n) * log(5/4)^(n - 1/2)). - Vaclav Kotesovec, Aug 27 2025

cp's OEIS Frontend

A377693 E.g.f. satisfies A(x) = (1 - log(1 - x) * A(x))^3.

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