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A081140 10th binomial transform of (0,0,1,0,0,0,...). 14
0, 0, 1, 30, 600, 10000, 150000, 2100000, 28000000, 360000000, 4500000000, 55000000000, 660000000000, 7800000000000, 91000000000000, 1050000000000000, 12000000000000000, 136000000000000000, 1530000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

Number of n-permutations (n=3) of 11 objects p, q, r, s, t, u, v, w, z, x, y with repetition allowed, containing exactly two u's. - Zerinvary Lajos, May 23 2008

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

MAPLE

seq(binomial(n+2, 2)*10^n, n=-2..16); # Zerinvary Lajos, May 23 2008

MATHEMATICA

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

PROG

(Sage)[lucas_number2(n, 10, 0)*binomial(n, 2)/10 ^2 for n in range(0, 18)] # Zerinvary Lajos, Mar 13 2009

(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

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Last modified September 23 04:39 EDT 2021. Contains 347609 sequences. (Running on oeis4.)