OFFSET
0,2
COMMENTS
The e.g.f. given below is (Sum_{m=0..3} A075513(4,m)*exp(5*(m+1)*x))/3!.
LINKS
Colin Barker, Table of n, a(n) for n = 0..767
Index entries for linear recurrences with constant coefficients, signature (50,-875,6250,-15000).
FORMULA
a(n) = (Sum_{m=0..3}A075513(4, m)*((m+1)*5)^n, m=0..3)/3!.
G.f.: 1/Product_{k=1..4}(1-5*k*x).
E.g.f.: (d^4/dx^4)((((exp(5*x)-1)/5)^4)/4!) = (-exp(5*x) + 24*exp(10*x) - 81*exp(15*x) + 64*exp(20*x))/3!.
a(n) = 50*a(n-1) - 875*a(n-2) + 6250*a(n-3) - 15000*a(n-4) for n>3. - Colin Barker, Dec 11 2015
MATHEMATICA
Table[5^n*(-1 + 3*2^(3+n) + 2^(6+2*n) - 3^(4+n))/6, {n, 0, 20}] (* Vaclav Kotesovec, Dec 12 2015 *)
PROG
(PARI) Vec(1/((1-5*x)*(1-10*x)*(1-15*x)*(1-20*x)) + O(x^30)) \\ Colin Barker, Dec 11 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 02 2002
STATUS
approved