A081913 -id:A081913 - cp's OEIS frontend

A081914 a(n) = 3^n*(n^3 - 3n^2 + 2n + 162)/162.

1, 3, 9, 28, 93, 333, 1269, 5022, 20169, 80919, 321489, 1259712, 4861701, 18482337, 69264477, 256154562, 935867601, 3381559083, 12096128601, 42874534116, 150706570221, 525729603573, 1821263718789, 6269238352998, 21454184419353

Offset: 0

Paul Barry, Mar 31 2003

Binomial transform of A081913 3rd binomial transform of (1,0,0,1,0,0,0,0,...). Case k=3 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.

Vincenzo Librandi, Table of n, a(n) for n = 0..150
Index entries for linear recurrences with constant coefficients, signature (12,-54,108,-81).

Cf. A081915.

[3^n*(n^3-3*n^2+2*n+162)/162: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011

CoefficientList[Series[(1 - 9x + 27x^2 - 26x^3)/(1-3x)^4 , {x, 0, 50}], x] (* Stefano Spezia, Sep 02 2018 *)
LinearRecurrence[{12,-54,108,-81},{1,3,9,28},30] (* Harvey P. Dale, Aug 01 2019 *)

a(n)=3^n*(n^3-3*n^2+2*n+162)/162 \\ Charles R Greathouse IV, Oct 07 2015

a(n) = 3^n*(n^3 - 3n^2 + 2n + 162)/162.

G.f.: (1 - 9x + 27x^2 - 26x^3)/(1-3x)^4.

A081917 a(0)=1, a(n)= n^(n-2)(7n^2-3n+2)/6 (n>0).

Original entry on oeis.org

1, 1, 4, 28, 272, 3375, 50976, 907578, 18612224, 432061533, 11200000000, 320680885976, 10051252125696, 342302635261067, 12586048547315712, 496928474121093750, 20968759865037029376, 941737183946729395897

Offset: 0

Paul Barry, Mar 31 2003

Main diagonal of square array defined by T(n,k)=k^n(n^3-3n^2+2n+6k^3)/(6k^3), in which rows have g.f. (1-3kx+3k^2x^2-(k^3-1)x^3)/(1-kx)^4.

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Cf. A050407, A081913, A081914, A081915, A081916.

cp's OEIS Frontend

A081914 a(n) = 3^n*(n^3 - 3n^2 + 2n + 162)/162.

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