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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
OFFSET
0,4
COMMENTS
Represents the mean of the second and fourth binomial transforms of C(n,2). Binomial transform of A082150
LINKS
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 07 2003
STATUS
approved