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A128625
Expansion of (1+3*x)/(1-5*x).
4
1, 8, 40, 200, 1000, 5000, 25000, 125000, 625000, 3125000, 15625000, 78125000, 390625000, 1953125000, 9765625000, 48828125000, 244140625000, 1220703125000, 6103515625000, 30517578125000, 152587890625000, 762939453125000, 3814697265625000, 19073486328125000
OFFSET
0,2
COMMENTS
Binomial transform of A102900(n+1).
Hankel transform is := 1,-24,0,0,0,0,0,0,0,0,0,... - Philippe Deléham, Nov 02 2008
FORMULA
a(n) = (8/5)*5^n - (3/5)*0^n.
a(0)=1, a(n) = Sum_{k=0..n} ((n+k)/n)*binomial(n,k)*2^(n-k)*3^k, n > 0.
E.g.f.: (8*exp(5*x) - 3)/5. - G. C. Greubel, Mar 12 2024
MATHEMATICA
CoefficientList[Series[(1 + 3 x)/(1 - 5 x), {x, 0, 50}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 21 2011 *)
Join[{1}, NestList[5#&, 8, 30]] (* or *) LinearRecurrence[{5}, {1, 8}, 30] (* Harvey P. Dale, Dec 23 2021 *)
PROG
(Magma) [n eq 0 select 1 else 8*5^(n-1): n in [0..50]]; // G. C. Greubel, Mar 12 2024
(SageMath) [(8*5^n - 3*int(n==0))//5 for n in range(51)] # G. C. Greubel, Mar 12 2024
CROSSREFS
Cf. A102900.
Sequence in context: A270283 A303391 A270730 * A037598 A037703 A272396
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 14 2007
STATUS
approved