A081911 -id:A081911 - cp's OEIS frontend

A081910 a(n) = 4^n*(n^2-n+32)/32.

1, 4, 17, 76, 352, 1664, 7936, 37888, 180224, 851968, 3997696, 18612224, 85983232, 394264576, 1795162112, 8120172544, 36507222016, 163208757248, 725849473024, 3212635537408, 14156212207616, 62122406969344, 271579372060672

Offset: 0

Paul Barry, Mar 31 2003

Binomial transform of A081909 4th binomial transform of (1,0,1,0,0,0,......). Case k=4 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 and Harvey P. Dale, Table of n, a(n) for n = 0..1000 [First 168 terms from _Vincenzo Librandi_]
Index entries for linear recurrences with constant coefficients, signature (12,-48,64).

Cf. A081911.

[4^n*(n^2-n+32)/32: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011

A081910:=n->4^n*(n^2-n+32)/32; seq(A081910(n), n=0..30); # Wesley Ivan Hurt, Mar 12 2014

Table[(4^n (n^2 - n + 32))/32, {n, 0, 30}] (* or *) LinearRecurrence[{12, -48, 64}, {1, 4, 17}, 30] (* Harvey P. Dale, Jan 18 2014 *)
CoefficientList[Series[(1 - 8 x + 17 x^2)/(1 - 4 x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 14 2014 *)

a(n) = 4^n*(n^2-n+32)/32; \\ Joerg Arndt, Mar 12 2014

a(n) = 4^n*(n^2-n+32)/32.
G.f.: (1-8*x+17*x^2)/(1-4*x)^3.
a(0)=1, a(1)=4, a(2)=17, a(n)=12*a(n-1)-48*a(n-2)+64*a(n-3). - Harvey P. Dale, Jan 18 2014

A081912 a(n) = 6^n*(n^2 - n + 72)/72.

Original entry on oeis.org

1, 6, 37, 234, 1512, 9936, 66096, 443232, 2985984, 20155392, 136048896, 917070336, 6167549952, 41358864384, 276451356672, 1841557856256, 12224809598976, 80871817347072, 533189772509184, 3503818505060352, 22952550207062016

Offset: 0

Paul Barry, Mar 31 2003

Binomial transform of A081911 6th binomial transform of (1,0,1,0,0,0,...). Case k=6 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 (18,-108,216).

[6^n*(n^2-n+72)/72: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011

a(n) = 6^n*(n^2 - n + 72)/72.

G.f.: (1 - 12x + 37x^2)/(1-6x)^3.

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

A081910 a(n) = 4^n*(n^2-n+32)/32.

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A081912 a(n) = 6^n*(n^2 - n + 72)/72.

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

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