A360471 E.g.f. satisfies A(x) = x * exp( 2*A(x) + x * exp(2*A(x)) ).
0, 1, 6, 75, 1476, 39805, 1366278, 56998179, 2800588808, 158420939193, 10140538486410, 724652822705119, 57187947315670284, 4939834587311520117, 463572330418586227790, 46965096302630022564315, 5108915146530700018466832, 593925863391217441843199089
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..337
Programs
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PARI
a(n) = sum(k=1, n, k^(n-k)*(2*n)^(k-1)*binomial(n, k));
Formula
a(n) = Sum_{k=1..n} k^(n-k) * (2*n)^(k-1) * binomial(n,k).
a(n) ~ 2^(n - 1/2) * s^n * n^(n-1) / (sqrt(2 + 1/s - 4*s) * (1 - 2*s)^n * exp(n*(1 - 2*s))), where s = 0.3875920123187127910093095185777835252050660050582... is the root of the equation 2*s*(1 + LambertW(s)) = 1. - Vaclav Kotesovec, Feb 17 2023