A093856 a(0)=1; a(1)=2; a(n+1) = 2*n*a(n) - a(n-1) for n >= 1.

1, 2, 3, 10, 57, 446, 4403, 52390, 729057, 11612522, 208296339, 4154314258, 91186617337, 2184324501830, 56701250430243, 1585450687544974, 47506819375918977, 1518632769341862290, 51586007338247398883

Offset

0,2

Comments

a(n) = (a(n-1) + a(n+1))/(2n). - Emeric Deutsch, Feb 03 2006

Links

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

Formula

a(-n) = (-1)^n * a(n). - Michael Somos, Jan 25 2014

a(n+1) ~ 1.0903447... * 2^n * n! * f(1/(4*n)) where f(x) = 1 + x + x^2/2! + 13*x^3/3! + 241*x^4/4! + 6201*x^5/5! + ...). - Michael Somos, Jan 26 2014

0 = a(n) * (a(n+2)) + a(n+1) * (-a(n+1) + 2*a(n+2) - a(n+3)) + a(n+2) * (a(n+2)) for all n in Z. - Michael Somos, Jan 25 2014

0 = u0 * u3 - u1 * (u2 + 2*u3) + u2 * (4*u2) where u0 = e.g.f. a(n), u1=u0', u2=u1', u3=u2'. - Michael Somos, Jan 25 2014

Example

a(3) = 2*2*a(2)-a(1) = 12-2 = 10.
G.f. = 1 + 2*x + 3*x^2 + 10*x^3 + 57*x^4 + 446*x^5 + 4403*x^6 + 52390*x^7 + ...

Maple

a[0]:=1: a[1]:=2: for n from 1 to 20 do a[n+1]:=2*n*a[n]-a[n-1] od: seq(a[n], n=0..20); # Emeric Deutsch, Feb 03 2006

Mathematica

RecurrenceTable[{a[0]==1, a[1]==2, a[n]==2(n-1)*a[n-1]-a[n-2]}, a, {n, 20}] (* Harvey P. Dale, May 31 2016 *)

Crossrefs

Sequence in context: A052561 A181927 A066526 * A173097 A088221 A206296

Adjacent sequences: A093853 A093854 A093855 * A093857 A093858 A093859

Keyword

easy,nonn

Author

Amarnath Murthy, Apr 19 2004

Extensions

More terms from Emeric Deutsch, Feb 03 2006

Status

approved