A082151 A transform of C(n,2).

0, 0, 1, 12, 102, 760, 5295, 35364, 228956, 1445616, 8936685, 54252220, 324214242, 1911205608, 11132579003, 64170616020, 366497915640, 2076171038176, 11676266706969, 65242364726124, 362433045180830, 2002838101907160, 11015341078090503, 60321223747375492

Offset

0,4

Comments

Represents the mean of the second and fourth binomial transforms of C(n,2). Binomial transform of A082150

Links

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

Index entries for linear recurrences with constant coefficients, signature (24,-237,1232,-3555,5400,-3375).

Formula

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

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

a(n) = x^2*(76*x^3 - 51*x^2 + 12*x - 1)/((1-3*x)^3*(5*x-1)^3).

E.g.f.: x^2*exp(4*x)*cosh(x)/2.

Mathematica

CoefficientList[Series[(x^2/(1-5*x)^3 + x^2/(1-3*x)^3)/2, {x, 0, 50}], x] (* or *) Table[Binomial[n, 2]*(3^(n-2) + 5^(n-2))/2, {n, 0, 30}] (* G. C. Greubel, Feb 10 2018 *)
LinearRecurrence[{24, -237, 1232, -3555, 5400, -3375}, {0, 0, 1, 12, 102, 760}, 30] (* Harvey P. Dale, Apr 10 2023 *)

Prog

(PARI) for(n=0, 30, print1(binomial(n, 2)*(3^(n-2) + 5^(n-2))/2, ", ")) \\ G. C. Greubel, Feb 10 2018
(Magma) [Binomial(n, 2)*(3^(n-2) + 5^(n-2))/2: n in [0..30]]; // G. C. Greubel, Feb 10 2018

Crossrefs

Cf. A027472, A081135, A000217.

Sequence in context: A344279 A022736 A261483 * A125375 A217057 A356836

Adjacent sequences: A082148 A082149 A082150 * A082152 A082153 A082154

Keyword

easy,nonn

Author

Paul Barry, Apr 07 2003

Status

approved