A081367 E.g.f.: exp(2*x)/sqrt(1-2*x).

1, 3, 11, 53, 345, 2947, 31411, 400437, 5927921, 99816515, 1882741659, 39310397557, 899919305929, 22410922177347, 603120939234755, 17441737474345973, 539390080299331809, 17762381612118471043

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..99

Formula

a(n) = Sum_{k = 0..n} A046716(n, k)*2^k. - Philippe Deléham, Jun 12 2004

a(n) = U(1/2,3/2+n,1)*2^n, where U is the confluent hypergeometric Kummer function U. - John M. Campbell, May 04 2011

D-finite with recurrence: a(n) = (2*n+1)*a(n-1) - 4*(n-1)*a(n-2). - Vaclav Kotesovec, Oct 13 2012

a(n) ~ 2^(n+1/2)*n^n/exp(n-1). - Vaclav Kotesovec, Oct 13 2012

G.f.: W(0)/(1-2*x), where W(k) = 1 - x*(k+1)/(x*(k+1) - (1-2*x)/W(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 03 2014

From Robert Israel, Nov 04 2014: (Start)

a(n) = 2^n * hypergeom([1/2,-n],[],-1).

G.f. satisfies (1-3*x+4*x^2)*g(x) + (-2*x^2+4*x^3)*g'(x) = 1. (End)

Maple

F:= gfun:-rectoproc({a(n) = (2*n+1)*a(n-1) - 4*(n-1)*a(n-2), a(0)=1, a(1)=3}, a(n), remember):
seq(F(n), n=0..30); # Robert Israel, Nov 04 2014

Mathematica

Table[HypergeometricU[1/2, 3/2 + n, 1]*2^n, {n, 0, 20}]
With[{nn=20}, CoefficientList[Series[Exp[2x]/Sqrt[1-2x], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 20 2015 *)

Prog

(PARI) a(n)=n!*polcoeff(exp(2*x)/sqrt(1-2*x)+O(x^(n+1)), n)

Crossrefs

Sequence in context: A121580 A321732 A224345 * A156171 A129093 A259106

Adjacent sequences: A081364 A081365 A081366 * A081368 A081369 A081370

Keyword

nonn

Author

Benoit Cloitre, May 10 2003

Status

approved