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A084902 a(n) = 5^(n-1)*n*(n+1)/2. 4
0, 1, 15, 150, 1250, 9375, 65625, 437500, 2812500, 17578125, 107421875, 644531250, 3808593750, 22216796875, 128173828125, 732421875000, 4150390625000, 23345947265625, 130462646484375, 724792480468750, 4005432128906250 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Binomial transform of A084901. Fourth binomial transform of heptagonal numbers A000566. Fifth binomial transform of (0,1,5,0,0,0,...).

Number of n-permutations of 6 objects u, v, w, z, x, y with repetition allowed, containing exactly two u's. Example: a(2)=15 because we have uuw, uuv, uuz, uux, uuy, uwu, uvu, uzu, uxu, uyu, wuu, vuu, zuu, xuu, yuu. - Zerinvary Lajos, Dec 30 2007

A shifted version of A081135. - R. J. Mathar, Sep 17 2008

LINKS

Table of n, a(n) for n=0..20.

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

FORMULA

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

MATHEMATICA

Table[5^(n-1)n (n+1)/2, {n, 0, 20}] (* or *) LinearRecurrence[{15, -75, 125}, {0, 1, 15}, 30] (* Harvey P. Dale, Sep 18 2018 *)

PROG

(PARI) a(n)=5^(n-1)*n*(n+1)/2 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A000566, A038243, A081135, A084901.

Sequence in context: A022739 A085375 A081135 * A021364 A323298 A206366

Adjacent sequences:  A084899 A084900 A084901 * A084903 A084904 A084905

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jun 10 2003

STATUS

approved

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Last modified May 5 19:09 EDT 2021. Contains 343573 sequences. (Running on oeis4.)