OFFSET
0,2
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..100
FORMULA
G.f.: Sum_{n>=0} (1 + n*x)^(n+1) / (2 + n*x)^(n+1). - Paul D. Hanna, Oct 26 2014
a(n) = n-th derivative of (1 + 2/x + 3/x^2)/2 at -1. - Luc Rousseau, May 03 2022
EXAMPLE
G.f.: A(x) = 1 + 2*x + 7*x^2 + 30*x^3 + 156*x^4 + 960*x^5 + 6840*x^6 + ...
where
A(x) = 1/2 + (1+x)^2/(2+x)^2 + (1+2*x)^3/(2+2*x)^3 + (1+3*x)^4/(2+3*x)^4 + (1+4*x)^5/(2+4*x)^5 + (1+5*x)^6/(2+5*x)^6 + (1+6*x)^7/(2+6*x)^7 + ...
MATHEMATICA
Join[{1}, Table[(n!(3n+1))/2, {n, 20}]] (* Harvey P. Dale, Jun 15 2011 *)
PROG
(PARI) { for (n=0, 100, a=(n!*(3*n + 1))/2; if (n==0, a=1); write("b066114.txt", n, " ", a) ) } \\ Harry J. Smith, Feb 01 2010
(PARI) \p200 \\ set precision
{A=Vec(sum(n=0, 600, (1.+n*x)^(n+1)/(2 + n*x +O(x^31))^(n+1)) )}
for(n=1, #A, print1(round(A[n]), ", ")) \\ Paul D. Hanna, Oct 26 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
George E. Antoniou, Dec 05 2001
STATUS
approved