OFFSET
0,3
COMMENTS
Generally, A(n,k) ~ n! * n * sum(t>=1, t^k*(t^2+t-1)/(t+2)!) = n! * n * ((Bell(k) - Bell(k+1) + sum(j=0..k, (-1)^j*(2^j*((2*k-j+1)/(j+1))-1) *Bell(k-j) *C(k,j))) *exp(1) - (-1)^k*(2^k-1)), where Bell(k) are Bell numbers A000110. Set k=10 for this sequence. - Vaclav Kotesovec, Sep 12 2013
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
a(n) ~ n! * (83342*exp(1)-1023)*n. - Vaclav Kotesovec, Sep 12 2013
MAPLE
a:= proc(n) option remember; `if`(n<5, [0, 1, 1026, 63152,
1424406][n+1], ((398*n^3-539*n^2-4964*n+24377)*a(n-1)
-(199*n^4+1057*n^3-12543*n^2+57436*n-31692)*a(n-2)
+(1017*n^4-7565*n^3+34942*n^2-38827*n-17617)*a(n-3)
-(n-3)*(1017*n^3-5258*n^2+21882*n-30370)*a(n-4)
+(n-3)*(n-4)*(199*n^2-1212*n+1877)*a(n-5))/
(199*n^2-778*n+792))
end:
seq(a(n), n=0..30);
MATHEMATICA
k=10; Table[n^k+Sum[t^k*n!*(n*(t^2+t-1)-t*(t^2-4)+1)/(t+2)!+Floor[t/n]*(1/(t*(t+3)+2)), {t, 1, n-1}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 12 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 10 2013
STATUS
approved