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

Author

J. C. George, May 12 2016

Keywords

• easy
• nonn

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

Mathematica

Table[Sum[Subfactorial[k] Subfactorial[n - k], {k, 0, n}], {n, 0, 30}] (* Emanuele Munarini, Oct 06 2017 *)

Formula

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

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