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A082151 A transform of C(n,2). 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 (list; graph; refs; listen; history; text; internal format)
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 *)

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: A304504 A022736 A261483 * A125375 A217057 A240462

Adjacent sequences:  A082148 A082149 A082150 * A082152 A082153 A082154

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 07 2003

STATUS

approved

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Last modified June 15 20:50 EDT 2019. Contains 324145 sequences. (Running on oeis4.)