A262601 a(n) = n!*(e*Gamma(n,1)*(n-1)+1).

1, 6, 66, 1176, 31320, 1174320, 59184720, 3866728320, 318176449920, 32215365100800, 3937433507884800, 571715345296972800, 97295556944518732800, 19183440644220345292800, 4338408884154346729728000, 1115590855925401950302208000, 323670093665823262135185408000, 105233239203100787701553799168000

Offset

1,2

Links

Table of n, a(n) for n=1..18.

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: A267080 A229002 A122020 * A329930 A367308 A271220

Adjacent sequences: A262598 A262599 A262600 * A262602 A262603 A262604

Keyword

nonn

Author

Karol A. Penson and Katarzyna Gorska, Sep 25 2015

Status

approved