A081141 11th binomial transform of (0,0,1,0,0,0,...).

0, 0, 1, 33, 726, 13310, 219615, 3382071, 49603708, 701538156, 9646149645, 129687123005, 1711870023666, 22254310307658, 285596982281611, 3624884775112755, 45569980029988920, 568105751040528536

Offset

0,4

Comments

Starting at 1, the three-fold convolution of A001020 (powers of 11).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (33,-363,1331).

Formula

a(n) = 33*a(n-1) - 363*a(n-2) + 1331*a(n-3), a(0) = a(1) = 0, a(2) = 1.

a(n) = 11^(n-2)*binomial(n, 2).

G.f.: x^2/(1 - 11*x)^3.

E.g.f.: (1/2)*exp(11*x)*x^2. - Franck Maminirina Ramaharo, Nov 23 2018

From Amiram Eldar, Jan 06 2022: (Start)

Sum_{n>=2} 1/a(n) = 22 - 220*log(11/10).

Sum_{n>=2} (-1)^n/a(n) = 264*log(12/11) - 22. (End)

Maple

seq((11)^(n-2)*binomial(n, 2), n=0..30); # G. C. Greubel, May 13 2021

Mathematica

LinearRecurrence[{33, -363, 1331}, {0, 0, 1}, 30] (* Harvey P. Dale, Dec 15 2014 *)

Prog

(Magma) [11^(n-2)*Binomial(n, 2): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011
(PARI) vector(20, n, n--; 11^(n-2)*binomial(n, 2)) \\ G. C. Greubel, Nov 23 2018
(Sage) [11^(n-2)*binomial(n, 2) for n in range(20)] # G. C. Greubel, Nov 23 2018

Crossrefs

Cf. A001020.

Sequences similar to the form q^(n-2)*binomial(n, 2): A000217 (q=1), A001788 (q=2), A027472 (q=3), A038845 (q=4), A081135 (q=5), A081136 (q=6), A027474 (q=7), A081138 (q=8), A081139 (q=9), A081140 (q=10), this sequence (q=11), A081142 (q=12), A027476 (q=15).

Sequence in context: A028022 A028020 A025130 * A021021 A164750 A100788

Adjacent sequences: A081138 A081139 A081140 * A081142 A081143 A081144

Keyword

easy,nonn

Author

Paul Barry, Mar 08 2003

Status

approved