OFFSET
1,2
FORMULA
a(n) is the sum of infinite series of the hypergeometric functions of type 2F0, in Maple notation: a(n)=sum(k*(n+k-1)!*hypergeom([k+1,k+1],[],-1),k=1..infinity),n=1,2,... .
a(n) = n!*(A000522(n-1)*(n-1)+1). - Jean-François Alcover, Sep 26 2015
MAPLE
seq(simplify(n!*(n*exp(1)*GAMMA(n, 1)-exp(1)*GAMMA(n, 1)+1)), n=1..18);
# GAMMA(n, 1) is the incomplete gamma function.
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson and Katarzyna Gorska, Sep 25 2015
STATUS
approved