A272988 Convolution of the sequence of derangement numbers A000166 with itself.
1, 0, 2, 4, 19, 92, 552, 3832, 30453, 272552, 2713710, 29752156, 356133959, 4620985700, 64600445812, 967927029168, 15473320537001, 262864036323600, 4728905854617562, 89808092596277364, 1795480569403712699, 37693097921348983852, 829024574048725950016, 19063166411687276701736
Offset: 0
Examples
For n = 4, we get 1*9 + 0*2 + 1*1 + 2*0 + 9*1 = 19.
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..440
Crossrefs
Cf. A000166.
Programs
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Mathematica
Table[Sum[Subfactorial[k] Subfactorial[n - k], {k, 0, n}], {n, 0, 30}] (* Emanuele Munarini, Oct 06 2017 *)
Formula
G.f.: ( 1/(1 + x) + Sum_{k>=1} k^k*x^k/(1 + (k + 1)*x)^(k+1) )^2. - Ilya Gutkovskiy, Apr 13 2017
a(n) ~ 2*exp(-1)*n!. - Vaclav Kotesovec, Apr 13 2017