A081127 11th binomial transform of (0,1,0,0,0,0,0,...).

0, 1, 22, 363, 5324, 73205, 966306, 12400927, 155897368, 1929229929, 23579476910, 285311670611, 3423740047332, 40799568897373, 483317970015034, 5696247503748615, 66835970710650416, 781145407680726737

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (22,-121).

Formula

a(n) = 22*a(n-1) - 121*a(n-2), with a(0)=0, a(1)=1.

a(n) = n*11^(n-1).

G.f.: x/(1-11*x)^2.

a(n) = A003415(11^n). - Bruno Berselli, Oct 22 2013

From Amiram Eldar, Oct 28 2020: (Start)

Sum_{n>=1} 1/a(n) = 11*log(11/10).

Sum_{n>=1} (-1)^(n+1)/a(n) = 11*log(12/11). (End)

E.g.f.: x*exp(11*x). - G. C. Greubel, Jan 16 2024

Mathematica

a[n_]:=n*11^(n-1); a[Range[0, 40]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011*)

Prog

(Magma) [n*11^(n-1): n in [0..30]]; // Vincenzo Librandi, Jun 06 2011
(SageMath) [11^(n-1)*n for n in range(31)] # G. C. Greubel, Jan 16 2024

Crossrefs

Cf. A003415, A038315, A053541, A081128.

Sequence in context: A001718 A199671 A253878 * A016196 A238318 A167120

Adjacent sequences: A081124 A081125 A081126 * A081128 A081129 A081130

Keyword

easy,nonn

Author

Paul Barry, Mar 07 2003

Status

approved