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A262601
a(n) = n!*(e*Gamma(n,1)*(n-1)+1).
0
1, 6, 66, 1176, 31320, 1174320, 59184720, 3866728320, 318176449920, 32215365100800, 3937433507884800, 571715345296972800, 97295556944518732800, 19183440644220345292800, 4338408884154346729728000, 1115590855925401950302208000, 323670093665823262135185408000, 105233239203100787701553799168000
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
Cf. A000522.
Sequence in context: A229002 A376098 A122020 * A329930 A367308 A271220
KEYWORD
nonn
AUTHOR
Karol A. Penson and Katarzyna Gorska, Sep 25 2015
STATUS
approved