A349599 E.g.f. satisfies: log(A(x)) = 1 - exp(-x*A(x)^2).

1, 1, 4, 29, 305, 4192, 70875, 1416781, 32551650, 841273527, 24032201213, 747395938962, 24946766300549, 880465276003861, 32274320771151308, 1197240324544640433, 42849289206116498093, 1304855947753532683776, 14954863230501575196551, -2798084168801754024136463

Offset: 0

Author

Seiichi Manyama, Nov 22 2021

Keywords

• sign

Comments

a(19) < 0.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..374

Crossrefs

Cf. A001761, A001763, A349598.

Cf. A349527, A349602.

Programs

PARI

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

Formula

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