A352683 a(n) = A352682(4, n).

1, 4, 5, 14, 42, 145, 566, 2446, 11547, 58980, 323458, 1892559, 11751904, 77101510, 532426225, 3857129474, 29229557534, 231113610537, 1902340920682, 16267763481746, 144260854186939, 1324431903156744, 12569419869410886, 123141802554934015, 1243798055506236156

Offset: 0

Author

Peter Luschny, Mar 30 2022

Keywords

• nonn

Crossrefs

Cf. A352682, A000110 (Bell), A040027 (Gould).

Programs

Julia

function A352683List(len)
    a = 4; P = BigInt[1]; T = BigInt[1]
    for n in 1:len-1
        T = vcat(T, a)
        P = cumsum(vcat(a, P))
        a = P[end]
    end
T end
A352683List(25) |> println

Formula

a(n) = 3*Gould(n - 1) + Bell(n) for n >= 1.

a(n) = Sum_{k=1..n} binomial(n-1, k-1)*a(n-k) for n >= 2.