A384514 Expansion of e.g.f. 6/(7 - exp(6*x)).
1, 1, 8, 78, 960, 14736, 272448, 5881968, 145105920, 4026744576, 124159039488, 4211132779008, 155814875873280, 6245695887446016, 269610827961212928, 12469729905669224448, 615184657168540631040, 32246522356406129197056, 1789714914567248392224768
Offset: 0
Keywords
Links
- Wikipedia, Polylogarithm.
Programs
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PARI
a(n) = (-6)^(n+1)*polylog(-n, 7)/7;
Formula
a(n) = (-6)^(n+1)/7 * Li_{-n}(7), where Li_{n}(x) is the polylogarithm function.
a(n) = 6^(n+1) * Sum_{k>=0} k^n * (1/7)^(k+1).
a(n) = Sum_{k=0..n} 6^(n-k) * k! * Stirling2(n,k).
a(n) = (1/7) * Sum_{k=0..n} 7^k * (-6)^(n-k) * k! * Stirling2(n,k) for n > 0.
a(0) = 1; a(n) = Sum_{k=1..n} 6^(k-1) * binomial(n,k) * a(n-k).
a(0) = 1; a(n) = a(n-1) + 7 * Sum_{k=1..n-1} (-6)^(k-1) * binomial(n-1,k) * a(n-k).