A082150 A transform of C(n,2).

0, 0, 1, 9, 60, 360, 2040, 11088, 58240, 297216, 1480320, 7223040, 34636800, 163657728, 763549696, 3523645440, 16107110400, 73016672256, 328570011648, 1468890021888, 6528375193600, 28862235279360, 126993714118656

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 *)
LinearRecurrence[{18, -132, 504, -1056, 1152, -512}, {0, 0, 1, 9, 60, 360}, 30] (* Harvey P. Dale, Jan 17 2022 *)

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