A081907 A sequence related to binomial(n+2, 2).

1, 8, 61, 450, 3240, 22896, 159408, 1096416, 7464960, 50388480, 337602816, 2247326208, 14874679296, 97955205120, 642150789120, 4192482779136, 27270729105408, 176789554200576, 1142549512519680, 7363096858460160

Offset

0,2

Comments

Binomial transform of A081894.

5th binomial transform of binomial(n+2, 2), A000217.

6th binomial transform of (1,2,1,0,0,0,...).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (18,-108,216).

Formula

a(n) = 6^n*(n^2 + 23*n + 72)/72.

G.f.: (1-5*x)^2/(1-6*x)^3.

E.g.f.: (2 + 4*x + x^2)*exp(6*x)/2. - G. C. Greubel, Oct 17 2018

Maple

seq(coeff(series((1-5*x)^2/(1-6*x)^3, x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 18 2018

Mathematica

Table[6^n*(n^2+23*n+72)/72, {n, 0, 50}] (* or *) LinearRecurrence[{18, -108, 216}, {1, 8, 61}, 50] (* G. C. Greubel, Oct 17 2018 *)

Prog

(PARI) vector(50, n, n--; 6^n*(n^2 +23*n +72)/72) \\ G. C. Greubel, Oct 17 2018
(Magma) [6^n*(n^2 +23*n +72)/72: n in [0..50]]; // G. C. Greubel, Oct 17 2018
(GAP) List([1..20], n->6^(n-1)*(n^2+21*n+50))/72; # Muniru A Asiru, Oct 18 2018

Crossrefs

Sequence in context: A247535 A283852 A283410 * A278596 A190976 A254602

Adjacent sequences: A081904 A081905 A081906 * A081908 A081909 A081910

Keyword

easy,nonn

Author

Paul Barry, Mar 30 2003

Status

approved