A367470 Expansion of e.g.f. 1 / (3 - 2 * exp(x))^2.
1, 4, 28, 268, 3244, 47404, 810988, 15891628, 350851564, 8615761324, 232911898348, 6872755977388, 219799913877484, 7572909749244844, 279630706025296108, 11016315458773541548, 461211305514352065004, 20448268640012928321964
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, 2^k*(k+1)!*stirling(n, k, 2));
Formula
a(n) = Sum_{k=0..n} 2^k * (k+1)! * Stirling2(n,k).
a(0) = 1; a(n) = 2*Sum_{k=1..n} (k/n + 1) * binomial(n,k) * a(n-k).
a(0) = 1; a(n) = 4*a(n-1) - 3*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k).
a(n) ~ sqrt(2*Pi) * n^(n + 3/2) / (9 * log(3/2)^(n+2) * exp(n)). - Vaclav Kotesovec, May 20 2025