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%I #10 May 08 2017 00:16:10
%S 1,6,28,104,336,992,2752,7296,18688,46592,113664,272384,643072,
%T 1499136,3457024,7897088,17891328,40239104,89915392,199753728,
%U 441450496,970981376,2126512128,4638900224,10083106816,21843935232,47177531392,101602820096,218238025728
%N Exponential convolution of odd numbers (A005408) with themselves.
%H M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72. Erratum 320 (2000), 210. [Link to arXiv version]
%H M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8)
%F O.g.f.: (1 + 4*x^2)/(1 - 2*x)^3.
%F E.g.f.: (1 + 2*x)^2*exp(2*x).
%F a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3).
%F a(n) = 2^n*(n^2 + n + 1).
%F a(n) = A000079(n)*A002061(n+1).
%F Binomial transform of A053755.
%t LinearRecurrence[{6, -12, 8}, {1, 6, 28}, 29]
%t Table[2^n (n^2 + n + 1), {n, 0, 28}]
%Y Cf. A000079, A002061, A005408, A053755, A128796 (exponential convolution of even numbers with themselves).
%K nonn,easy
%O 0,2
%A _Ilya Gutkovskiy_, Aug 17 2016
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