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A104098 a(n) = Sum_{k=1..n} binomial(n-1, k-1)*A008292(n, k) for n >= 1.

%I A104098 #30 Feb 10 2024 04:45:33
%S A104098 1,2,10,68,606,6612,85492,1277096,21641590,410144180,8595133548,
%T A104098 197346180792,4926442358124,132847425483528,3848398710032616,
%U A104098 119187270233781456,3929892162743796390,137444081992905303540,5082053733073190713660,198081684441819323760920
%N A104098 a(n) = Sum_{k=1..n} binomial(n-1, k-1)*A008292(n, k) for n >= 1.
%H A104098 Vaclav Kotesovec, <a href="/A104098/b104098.txt">Table of n, a(n) for n = 1..201</a>
%F A104098 a(n) ~ sqrt(3) * 2^(n-1) * n^n / exp(n). - _Vaclav Kotesovec_, Oct 09 2020, modified for offset 1, Oct 29 2023
%e A104098    1 = 1*1
%e A104098    2 = 1*1 +  1*1
%e A104098   10 = 1*1 +  2*4 + 1*1
%e A104098   68 = 1*1 + 3*11 + 3*11 + 1*1
%e A104098   ...
%p A104098 a := n -> local k; add(binomial(n - 1, k - 1) * combinat:-eulerian1(n, k - 1), k = 1..n): seq(a(n), n = 1..20);  # _Peter Luschny_, Oct 29 2023
%t A104098 Table[Sum[Binomial[n-1,k-1] * Sum[(-1)^j * (k-j)^n * Binomial[n+1,j], {j, 0, k}], {k, 1, n}], {n, 1, 20}] (* _Vaclav Kotesovec_, Oct 09 2020 *)
%Y A104098 Cf. A008292, A011818.
%K A104098 nonn
%O A104098 1,2
%A A104098 _Paul D. Hanna_, Mar 29 2006
%E A104098 Offset changed by _Georg Fischer_, Oct 29 2023