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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
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
Sequence in context: A344279 A022736 A261483 * A125375 A217057 A356836
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 07 2003
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)