A081916 - OEIS

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A081916

a(n) = 5^n*(n^3 - 3n^2 + 2n + 750)/750.

1, 5, 25, 126, 645, 3375, 18125, 100000, 565625, 3265625, 19140625, 113281250, 673828125, 4013671875, 23876953125, 141601562500, 836181640625, 4913330078125, 28717041015625, 166931152343750, 965118408203125

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OFFSET

0,2

COMMENTS

Binomial transform of A081915. 5th binomial transform of (1,0,0,1,0,0,0,0,...). Case k=5 where a(n,k) = k^n*(n^3 - 3n^2 + 2n + 6k^3)/(6k^3), with g.f. (1 - 3kx + 3k^2x^2 - (k^3-1)x^3)/(1-kx)^4.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..150

Index entries for linear recurrences with constant coefficients, signature (20,-150,500,-625).

FORMULA

a(n) = 5^n*(n^3 - 3n^2 + 2n + 750)/750.

G.f.: (1 - 15x + 75x^2 - 124x^3)/(1-5x)^4.

MATHEMATICA

a[n_]:= 5^n*(n^3 - 3n^2 + 2n + 750)/750 ; Array[a, 40, 0] (* or *)

CoefficientList[Series[(1 - 15x + 75x^2 - 124x^3)/(1-5x)^4 , {x, 0, 40}], x] (* Stefano Spezia, Sep 02 2018 *)

LinearRecurrence[{20, -150, 500, -625}, {1, 5, 25, 126}, 30] (* Harvey P. Dale, Jun 29 2021 *)

PROG

(Magma) [5^n*(n^3-3*n^2+2*n+750)/750: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011