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 A082150 A transform of C(n,2). 3
 0, 0, 1, 9, 60, 360, 2040, 11088, 58240, 297216, 1480320, 7223040, 34636800, 163657728, 763549696, 3523645440, 16107110400, 73016672256, 328570011648, 1468890021888, 6528375193600, 28862235279360, 126993714118656 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Represents the mean of the first and third binomial transforms of C(n,2) Binomial transform of A082149. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (18,-132,504,-1056,1152,-512). FORMULA a(n) = C(n, 2)*(2^(n-2) + 4^(n-2))/2. G.f.: (x^2/(1-2*x)^3 + x^2/(1-4*x)^3)/2. G.f.: x^2*(36*x^3 - 30*x^2 + 9*x-1)/((1 - 2*x)^3*(4*x - 1)^3). E.g.f.: x^2*exp(3*x)*cosh(x)/2. From Bruno Berselli, Feb 12 2018: (Start) E.g.f.: x^2*(1 + exp(2*x))*exp(2*x)/4. a(n) = 2^(n-4)*(2^(n-2) + 1)*(n - 1)*n. (End) MAPLE A082150:=[seq(binomial(n, 2)*(2^(n-2)+4^(n-2))/2, n=0..23)]; # Muniru A Asiru, Feb 12 2018 MATHEMATICA CoefficientList[Series[(x^2/(1-2*x)^3 + x^2/(1-4*x)^3)/2, {x, 0, 50}], x] (* or *) Table[Binomial[n, 2]*(2^(n-2) + 4^(n-2))/2, {n, 0, 30}] (* G. C. Greubel, Feb 10 2018 *) PROG (PARI) for(n=0, 30, print1(binomial(n, 2)*(2^(n-2) + 4^(n-2))/2, ", ")) \\ G. C. Greubel, Feb 10 2018 (MAGMA) [Binomial(n, 2)*(2^(n-2) + 4^(n-2))/2: n in [0..30]]; // G. C. Greubel, Feb 10 2018 (GAP) List([0..23], n-> Binomial(n, 2)*(2^(n-2)+4^(n-2))/2); # Muniru A Asiru, Feb 12 2018 (Maxima) makelist(2^(n-4)*(2^(n-2)+1)*(n-1)*n, n, 0, 30); /* Bruno Berselli, Feb 13 2018 */ CROSSREFS Cf. A082151, A038845, A001788, A000217. Sequence in context: A081904 A085373 A241976 * A026785 A153820 A009139 Adjacent sequences:  A082147 A082148 A082149 * A082151 A082152 A082153 KEYWORD nonn,easy AUTHOR Paul Barry, Apr 07 2003 STATUS approved

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Last modified June 19 11:23 EDT 2019. Contains 324219 sequences. (Running on oeis4.)