OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (15, -50).
FORMULA
a(n) = (5^n)*Stirling2(n+2, 2), n >= 0, with Stirling2(n, m) = A008277(n, m).
a(n) = -5^n + 2*10^n.
G.f.: 1/((1-5*x)*(1-10*x)).
E.g.f.: (d^2/dx^2)((((exp(5*x)-1)/5)^2)/2!) = -exp(5*x) + 2*exp(10*x).
Sum_{k=1..n} 5^(k-1)*5^(n-k)*binomial(n, k). - Zerinvary Lajos, Sep 24 2006
a(0)=1, a(n) = 10*a(n-1) + 5^n. - Vincenzo Librandi, Feb 09 2011
MATHEMATICA
Join[{a=1, b=15}, Table[c=15*b-50*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
LinearRecurrence[{15, -50}, {1, 15}, 20] (* Harvey P. Dale, Aug 08 2023 *)
PROG
(PARI) Vec(1/((1-5*x)(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 25 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved