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%I #7 Jul 11 2014 07:42:35
%S 1,1,11,226,17001,2671876,1242300001,1250703890626,3363964848750001,
%T 20117722302277734376,302329590133667187500001,
%U 10299774530356369019736328126,846958190132982653045661328125001,160085716663876329020695686381591796876
%N E.g.f.: Sum_{n>=0} exp(n*5^n*x) * x^n/n!.
%H Vaclav Kotesovec, <a href="http://oeis.org/A244820/a244820.pdf">Asymptotic of sequences A244820, A244821 and A244822</a>
%F a(n) = Sum_{k=0..n} C(n,k) * k^(n-k) * 5^(k*(n-k)).
%F O.g.f.: Sum_{n>=0} x^n/(1 - n*5^n*x)^(n+1).
%t Flatten[{1, Table[Sum[Binomial[n, k]*k^(n-k)*5^(k*(n-k)), {k, 0, n}], {n, 1, 20}]}]
%o (PARI) {a(n) = sum(k=0, n, binomial(n, k) * k^(n-k) * 5^(k*(n-k)) )}
%o for(n=0, 20, print1(a(n), ", "))
%Y Cf. A244820, A244821, A244822.
%K nonn,easy
%O 0,3
%A _Vaclav Kotesovec_, Jul 11 2014
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