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10th iteration of the hyperbinomial transform on the sequence of 1's.
2

%I #8 Oct 18 2013 15:11:55

%S 1,11,141,2081,34961,661601,13970521,326429401,8377176001,

%T 234573153281,7125155956601,233554674134441,8223284332647361,

%U 309711995280132001,12430859603012736601,529915231307371964201,23918971999180778999681,1139982481554110359552001

%N 10th iteration of the hyperbinomial transform on the sequence of 1's.

%C See A088956 for the definition of the hyperbinomial transform.

%H Alois P. Heinz, <a href="/A218502/b218502.txt">Table of n, a(n) for n = 0..150</a>

%F E.g.f.: exp(x) * (-LambertW(-x)/x)^10.

%F a(n) = Sum_{j=0..n} 10 * (n-j+10)^(n-j-1) * C(n,j).

%F Hyperbinomial transform of A218501.

%F a(n) ~ 10*exp(10+exp(-1))*n^(n-1). - _Vaclav Kotesovec_, Oct 18 2013

%p a:= n-> add(10*(n-j+10)^(n-j-1)*binomial(n,j), j=0..n):

%p seq (a(n), n=0..20);

%t Table[Sum[10*(n-j+10)^(n-j-1)*Binomial[n,j],{j,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 18 2013 *)

%Y Column k=10 of A144303.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Oct 30 2012