A088991 - OEIS

A088991

Derangement numbers d(n,4) where d(n,k) = k(n-1)(d(n-1,k) + d(n-2,k)), with d(0,k) = 1 and d(1,k) = 0.

1, 0, 4, 32, 432, 7424, 157120, 3949056, 114972928, 3805503488, 141137150976, 5797706178560, 261309106499584, 12821127008550912, 680286677982625792, 38814037079505895424, 2369659425449311272960, 154142301601844298776576, 10642813349855965483368448

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OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

Inverse binomial transform of A007696. E.g.f.: exp(-x)/(1-4*x)^(1/4). - Vladeta Jovovic, Dec 17 2003

a(n) ~ n^(n-1/4) * Gamma(3/4) * 4^n / (sqrt(Pi)*exp(n+1/4)). - Vaclav Kotesovec, Oct 08 2013

MATHEMATICA

CoefficientList[Series[E^(-x)/(1-4*x)^(1/4), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 08 2013 *)

CROSSREFS

Cf. A000166, A053871, A033030, A088992.

Sequence in context: A322735 A140178 A366685 * A009668 A005121 A327379

Adjacent sequences: A088988 A088989 A088990 * A088992 A088993 A088994

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 02 2003

STATUS

approved