A384523 Expansion of e.g.f. 3/(7 - 4*exp(3*x)).
1, 4, 44, 708, 15180, 406884, 13087404, 491114628, 21062220300, 1016197112484, 54476506976364, 3212426755972548, 206654933095516620, 14401921040252826084, 1080885666078491553324, 86916516692600836638468, 7455102038197447378720140, 679412933203279242481083684
Offset: 0
Keywords
Links
- Wikipedia, Polylogarithm.
Programs
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PARI
a(n) = (-3)^(n+1)*polylog(-n, 7/4)/7;
Formula
a(n) = (-3)^(n+1)/7 * Li_{-n}(7/4), where Li_{n}(x) is the polylogarithm function.
a(n) = 3^(n+1)/7 * Sum_{k>=0} k^n * (4/7)^k.
a(n) = Sum_{k=0..n} 4^k * 3^(n-k) * k! * Stirling2(n,k).
a(n) = (4/7) * Sum_{k=0..n} 7^k * (-3)^(n-k) * k! * Stirling2(n,k) for n > 0.
a(0) = 1; a(n) = 4 * Sum_{k=1..n} 3^(k-1) * binomial(n,k) * a(n-k).
a(0) = 1; a(n) = 4 * a(n-1) + 7 * Sum_{k=1..n-1} (-3)^(k-1) * binomial(n-1,k) * a(n-k).