OFFSET
0,2
REFERENCES
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 83.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 0..100
FORMULA
E.g.f.: A(x) = exp(-x)/(1-5x) satisfies (1-5x)A' - (4+5x)A = 0. - Gheorghe Coserea, Aug 06 2015
a(n+1) = (5n+4) a(n) + 5n a(n-1). - Gheorghe Coserea, Aug 06 2015
a(n) = 5^n*exp(-1/5)*Gamma(n+1,-1/5), where Gamma is the incomplete Gamma function. - Robert Israel, Aug 06 2015
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (5*k - 1) * a(n-k). - Ilya Gutkovskiy, Jan 17 2020
MAPLE
f:= gfun:-rectoproc({a(n+1) = (5*n+4)* a(n) + 5*n*a(n-1), a(0)=1, a(1)=4}, a(n), remember):
seq(f(n), n=0..30); # Robert Israel, Aug 06 2015
MATHEMATICA
nn = 20; Range[0, nn]! CoefficientList[Series[Exp[-x]/(1 - 5 x), {x, 0, nn}], x] (* T. D. Noe, Aug 17 2012 *)
PROG
(PARI) x='x+O('x^33); Vec(serlaplace(exp(-x)/(1-5*x))) \\ Gheorghe Coserea, Aug 06 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved