A384521 Expansion of e.g.f. 5/(7 - 2*exp(5*x)).
1, 2, 18, 218, 3474, 69290, 1659330, 46359770, 1480241970, 53171142410, 2122154748450, 93168872862650, 4462242691496850, 231524863130863850, 12936797161953970050, 774495903492069700250, 49458416187322116299250, 3355754824852804221058250, 241081466990843266748993250
Offset: 0
Keywords
Links
- Wikipedia, Polylogarithm.
Programs
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PARI
a(n) = (-5)^(n+1)*polylog(-n, 7/2)/7;
Formula
a(n) = (-5)^(n+1)/7 * Li_{-n}(7/2), where Li_{n}(x) is the polylogarithm function.
a(n) = 5^(n+1)/7 * Sum_{k>=0} k^n * (2/7)^k.
a(n) = Sum_{k=0..n} 2^k * 5^(n-k) * k! * Stirling2(n,k).
a(n) = (2/7) * Sum_{k=0..n} 7^k * (-5)^(n-k) * k! * Stirling2(n,k) for n > 0.
a(0) = 1; a(n) = 2 * Sum_{k=1..n} 5^(k-1) * binomial(n,k) * a(n-k).
a(0) = 1; a(n) = 2 * a(n-1) + 7 * Sum_{k=1..n-1} (-5)^(k-1) * binomial(n-1,k) * a(n-k).