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A272988 Convolution of the sequence of derangement numbers A000166 with itself. 1

%I

%S 1,0,2,4,19,92,552,3832,30453,272552,2713710,29752156,356133959,

%T 4620985700,64600445812,967927029168,15473320537001,262864036323600,

%U 4728905854617562,89808092596277364,1795480569403712699,37693097921348983852,829024574048725950016,19063166411687276701736

%N Convolution of the sequence of derangement numbers A000166 with itself.

%H Vaclav Kotesovec, <a href="/A272988/b272988.txt">Table of n, a(n) for n = 0..440</a>

%F a(n) = Sum_{i=0..n} A000166(i)*A000166(n-i).

%F G.f.: ( 1/(1 + x) + Sum_{k>=1} k^k*x^k/(1 + (k + 1)*x)^(k+1) )^2. - _Ilya Gutkovskiy_, Apr 13 2017

%F a(n) ~ 2*exp(-1)*n!. - _Vaclav Kotesovec_, Apr 13 2017

%e For n = 4, we get 1*9 + 0*2 + 1*1 + 2*0 + 9*1 = 19.

%t Table[Sum[Subfactorial[k] Subfactorial[n - k], {k, 0, n}], {n, 0, 30}] (* _Emanuele Munarini_, Oct 06 2017 *)

%Y Cf. A000166.

%K easy,nonn

%O 0,3

%A _J. C. George_, May 12 2016

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Last modified November 14 15:07 EST 2018. Contains 317208 sequences. (Running on oeis4.)