A081140 10th binomial transform of (0,0,1,0,0,0,...).

0, 0, 1, 30, 600, 10000, 150000, 2100000, 28000000, 360000000, 4500000000, 55000000000, 660000000000, 7800000000000, 91000000000000, 1050000000000000, 12000000000000000, 136000000000000000, 1530000000000000000

Offset

0,4

Comments

Starting at 1, the three-fold convolution of A011557 (powers of 10).

Links

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

Index entries for linear recurrences with constant coefficients, signature (30,-300,1000).

Formula

a(n) = 30*a(n-1) - 300*a(n-2) + 1000*a(n-3), a(0)=a(1)=0, a(2)=1.

a(n) = 10^(n-2)*binomial(n, 2).

G.f.: x^2/(1-10*x)^3.

E.g.f.: (x^2/2)*exp(10*x). - G. C. Greubel, May 13 2021

From Amiram Eldar, Jan 06 2022: (Start)

Sum_{n>=2} 1/a(n) = 20 - 180*log(10/9).

Sum_{n>=2} (-1)^n/a(n) = 220*log(11/10) - 20. (End)

Mathematica

Table[10^(n-2)*Binomial[n, 2], {n, 0, 30}] (* G. C. Greubel, May 13 2021 *)

Prog

(Magma) [10^n* Binomial(n+2, 2): n in [-2..20]]; // Vincenzo Librandi, Oct 16 2011

Crossrefs

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), this sequence (q=10), A081141 (q=11), A081142 (q=12), A027476 (q=15).

Sequence in context: A028052 A024445 A026308 * A131206 A020982 A024436

Adjacent sequences: A081137 A081138 A081139 * A081141 A081142 A081143

Keyword

easy,nonn

Author

Paul Barry, Mar 08 2003

Status

approved