|
| |
|
|
A053486
|
|
E.g.f.: exp(3x)/(1-x).
|
|
11
| |
|
|
1, 4, 17, 78, 393, 2208, 13977, 100026, 806769, 7280604, 72865089, 801693126, 9620848953, 125072630712, 1751021612937, 26265338542962, 420245459734113, 7144172944620084, 128595113390582001, 2443307155583319486, 48866143115153174121
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
LINKS
| 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 4's on the diagonal and 1's elsewhere. a(n) = Sum(k=0..n, A008290(n, k)*4^k). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 12 2003
a(n) = Sum[(n! / k!) * 3^k {k=0...n}] - Ross La Haye (rlahaye(AT)new.rr.com), Sep 21 2004
a(n)=sum{k=0..n, k!*C(n, k)3^(n-k)}; - Paul Barry (pbarry(AT)wit.ie), Apr 22 2005
G.f.: hypergeom([1,1],[],x/(1-3*x))/(1-3*x) - Mark van Hoeij, Nov 08 2011
Conjecture: -a(n) +(n+3)*a(n-1) +3*(1-n)*a(n-2)=0. - R. J. Mathar, Nov 14 2011
E.g.f.: exp(3x)/(1-x)=1/E(0); E(k)=1-x/(1-3/(3+(k+1)/E(k+1))) ; (continued fraction). - Sergei N. Gladkovskii, Nov 21 2011
|
|
|
MAPLE
| restart: G(x):=exp(3*x)/(1-x): g[0]:=G(x): for n from 1 to 20 do g[n]:=diff(g[n-1], x) od: x:=0: seq(g[n], n=0..20); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 03 2009]
|
|
|
CROSSREFS
| Cf. A008290.
Sequence in context: A123952 A005494 A193782 * A151249 A110307 A206228
Adjacent sequences: A053483 A053484 A053485 * A053487 A053488 A053489
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 15 2000
|
| |
|
|
