A081912 -id:A081912 - cp's OEIS frontend

A081911 a(n) = 5^n*(n^2 - n + 50)/50.

1, 5, 26, 140, 775, 4375, 25000, 143750, 828125, 4765625, 27343750, 156250000, 888671875, 5029296875, 28320312500, 158691406250, 885009765625, 4913330078125, 27160644531250, 149536132812500, 820159912109375

Offset: 0

Paul Barry, Mar 31 2003

Binomial transform of A081910 5th binomial transform of (1,0,1,0,0,0,...). Case k=5 where a(n,k) = k^n*(n^2 - n + 2k^2)/(2k^2) with g.f. (1 - 2kx + (k^2+1)x^2)/(1-kx)^3.

Vincenzo Librandi, Table of n, a(n) for n = 0..150
Index entries for linear recurrences with constant coefficients, signature (15,-75,125).

Cf. A081912.

[5^n*(n^2-n+50)/50: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011

Table[5^n(n^2-n+50)/50,{n,0,20}] (* or *) LinearRecurrence[{15,-75,125},{1,5,26},20] (* Harvey P. Dale, Jul 22 2011 *)

a(n)=5^n*(n^2-n+50)/50 \\ Charles R Greathouse IV, Oct 07 2015

a(n) = 5^n*(n^2 - n + 50)/50.
G.f.: (1 - 10x + 26x^2)/(1-5x)^3.
a(n) = 15*a(n-1) - 75*a(n-2) + 125*a(n-3); a(0)=1, a(1)=5, a(2)=26. - _Harvey P. Dale, Jul 22 2011

A081918 a(0) = 1; a(n) = n^(n-1)(3n-1)/2 (n>0).

Original entry on oeis.org

1, 1, 5, 36, 352, 4375, 66096, 1176490, 24117248, 559607373, 14500000000, 414998793616, 13002646487040, 442663617327139, 16271152851709952, 642244372558593750, 27093655358260903936, 1216529796891671712025

Offset: 0

Paul Barry, Mar 31 2003

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

Vincenzo Librandi, Table of n, a(n) for n = 0..101

Cf. A000124, A081908, A081909, A081910, A081911, A081912.

a(0)=1, a(n)=a(n)=n^n(n^2-n+2n^2)/(2n^2), n>0.

cp's OEIS Frontend

A081911 a(n) = 5^n*(n^2 - n + 50)/50.

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