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A053487 E.g.f.: exp(4x)/(1-x). 11
1, 5, 26, 142, 824, 5144, 34960, 261104, 2154368, 19651456, 197563136, 2177388800, 26145442816, 339957865472, 4759678552064, 71396252022784, 1142344327331840, 19419870744510464, 349557742120665088, 6641597375170543616, 132831948602922500096 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the binomial transform of A053486. More generally, for every integer k, the sequence whose e.g.f is exp((k+1)*x)/(1-x) is the binomial transform of the sequence whose e.g.f is exp(k*x)/(1-x). - Groux Roland, Mar 23 2011

LINKS

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

J. W. Layman, The Hankel Transform and Some of its Properties, J. Integer Sequences, 4 (2001), #01.1.5.

FORMULA

a(n) is the permanent of the n X n matrix with 5's on the diagonal and 1's elsewhere. a(n) = Sum_{k=0..n} A008290(n, k)*5^k. - Philippe Deléham, Dec 12 2003

E.g.f.: exp(4x)/(1-x)=1/E(0); E(k)=1-x/(1-4/(4+(k+1)/E(k+1))); (continued fraction). - Sergei N. Gladkovskii, Nov 21 2011

G.f.: 1/Q(0), where Q(k)= 1 - 4*x - x*(k+1)/(1-x*(k+1)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Apr 19 2013

a(n) ~ n! * exp(4). - Vaclav Kotesovec, Jun 21 2013

a(n) = exp(4)*Gamma(n+1,4). - Gerry Martens, Jul 24 2015

MAPLE

restart:F(x):=exp(4*x)/(1-x): f[0]:=F(x): for n from 1 to 20 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..20); # Zerinvary Lajos, Apr 03 2009

MATHEMATICA

With[{nn=30}, CoefficientList[Series[Exp[4x]/(1-x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jun 09 2013 *)

CROSSREFS

Sequence in context: A182401 A104498 A045379 * A277957 A183161 A263134

Adjacent sequences:  A053484 A053485 A053486 * A053488 A053489 A053490

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 15 2000

STATUS

approved

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Last modified May 30 08:40 EDT 2020. Contains 334712 sequences. (Running on oeis4.)