(MAGMAMagma) I:=[5, 39]; [1] cat [n le 2 select I[n] else (6*n-1) * Self(n-1) - (3*n-2)^2 * Self(n-2) : n in [1..30]]; // Vincenzo Librandi, Aug 30 2015
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Comment by R. J. Mathar, Oct 01 2016 : (Start):
The k-th elementary symmetric functions of the integers 1+j*3, j=0..n-1, form a triangle T(n,k), 0 <= k <= n, n >= 0:
For n >= 1, a(n-1) = 3^(n-1)*n!*sum(Sum_{k=0..n-1} binomial(k-2/3, k)/(n-k), k = 0..n-1). - Milan Janjic, Dec 14 2008, corrected by Peter Bala, Oct 08 2013
E.g.f.: (3 - log(1-3*x))/(3*(1-3*x)^(4/3)). - Robert Israel, Aug 30 2015
Boas-Buck type recurrence: a(0) = 1 and for n >= 1: a(n) = ((n+1)!/n) * Sum_{p=1..n} 3^(n-p)*(1 + 3*beta(n-p))*a(p-1)/p!, with beta(k) = A002208(k+1) / A002209(k+1). Proof from a(n) = A286718(n+1, 1). - Wolfdieter Lang, Aug 09 2017
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Boas-Buck type recurrence: a(0) = 1 and for n >= 1: a(n) = ((n+1)!/n) * Sum_{p=1..n} 3^(n-p)*(1 + 3*beta(n-p))*a(p-1)/p!, with beta(k) = A002208(k+1) / A002209(k+1). Proof from a(n) = A286718(n+1, 1). - Wolfdieter Lang, Aug 09 2017
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