A384435 Expansion of e.g.f. 2/(5 - 3*exp(2*x)).
1, 3, 24, 282, 4416, 86448, 2030784, 55656912, 1743277056, 61427981568, 2405046994944, 103579443604992, 4866448609591296, 247692476576575488, 13576823521525653504, 797345878311609526272, 49948684871884896731136, 3324530341927517641310208, 234293439367907438337982464
Offset: 0
Keywords
Links
- Wikipedia, Polylogarithm.
Programs
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PARI
a(n) = (-2)^(n+1)*polylog(-n, 5/3)/5;
Formula
a(n) = (-2)^(n+1)/5 * Li_{-n}(5/3), where Li_{n}(x) is the polylogarithm function.
a(n) = 2^(n+1)/5 * Sum_{k>=0} k^n * (3/5)^k.
a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * k! * Stirling2(n,k).
a(n) = (3/5) * A201366(n) = (3/5) * Sum_{k=0..n} 5^k * (-2)^(n-k) * k! * Stirling2(n,k) for n > 0.
a(0) = 1; a(n) = 3 * Sum_{k=1..n} 2^(k-1) * binomial(n,k) * a(n-k).
a(0) = 1; a(n) = 3 * a(n-1) + 5 * Sum_{k=1..n-1} (-2)^(k-1) * binomial(n-1,k) * a(n-k).