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%I #6 May 07 2019 04:01:20
%S 0,0,2,30,398,5430,79022,1238790,20944478,381167670,7443745742,
%T 155454939750,3459933837758,81801569650710,2048133412585262,
%U 54153668865539910,1508122968767710238,44130728380569410550
%N Exponential convolution of A069321(n) with itself, where we set A069321(0)=0.
%F a(n)=Sum(C(n, k)Sum(i!i Stirling2(k, i), i=1, .., k)Sum(i!i Stirling2(n-k, i), i=1, .., n-k), k=0, .., n)
%F E.g.f.: (exp(x)-1)^2 / (2-exp(x))^4. - _Vaclav Kotesovec_, May 07 2019
%F a(n) ~ n! * n^3 / (96 * log(2)^(n+4)). - _Vaclav Kotesovec_, May 07 2019
%t Table[ Sum[Binomial[n, k]Sum[i!i StirlingS2[k, i], {i, 1, k}]Sum[i!i StirlingS2[n - k, i], {i, 1, n - k}], {k, 0, n}], {n, 0, 20}]
%t nmax = 20; CoefficientList[Series[(E^x-1)^2 / (2-E^x)^4, {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, May 07 2019 *)
%K easy,nonn
%O 0,3
%A Mario Catalani (mario.catalani(AT)unito.it), Jan 01 2004
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