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A081135 5th binomial transform of (0,0,1,0,0,0,...). 9
0, 0, 1, 15, 150, 1250, 9375, 65625, 437500, 2812500, 17578125, 107421875, 644531250, 3808593750, 22216796875, 128173828125, 732421875000, 4150390625000, 23345947265625, 130462646484375, 724792480468750 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Starting at 1, three-fold convolution of A000351 (powers of 5).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (15,-75,125).

FORMULA

a(n) = 15a(n-1) - 75a(n-2) + 125a(n-3), a(0)=a(1)=0, a(2)=1.

a(n) = 5^(n-2)*binomial(n, 2).

G.f.: x^2/(1-5x)^3.

MAPLE

seq(n*(n-1)*5^(n-2)/2, n=0..20); # Zerinvary Lajos, May 03 2007

MATHEMATICA

CoefficientList[Series[x^2 / (1 - 5 x)^3, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)

LinearRecurrence[{15, -75, 125}, {0, 0, 1}, 30] (* Harvey P. Dale, Sep 13 2017 *)

PROG

(Sage) [lucas_number2(n, 5, 0)*binomial(n, 2)/5^2 for n in xrange(0, 21)] # Zerinvary Lajos, Mar 12 2009

(MAGMA) [5^(n-2)*Binomial(n, 2): n in [0..25]]; // Vincenzo Librandi, Aug 06 2013

CROSSREFS

Cf. A038845, A027472, A081136.

Sequence in context: A121035 A022739 A085375 * A084902 A021364 A323298

Adjacent sequences:  A081132 A081133 A081134 * A081136 A081137 A081138

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 08 2003

STATUS

approved

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Last modified November 18 07:22 EST 2019. Contains 329252 sequences. (Running on oeis4.)