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

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..440

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

Example

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

Mathematica

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

Crossrefs

Cf. A000166.

Sequence in context: A362350 A289269 A363303 * A168246 A212923 A058130

Adjacent sequences: A272985 A272986 A272987 * A272989 A272990 A272991

Keyword

easy,nonn

Author

J. C. George, May 12 2016

Status

approved