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%I #18 Jul 30 2023 14:31:54
%S 1,9,44,170,576,1792,5248,14688,39680,104192,267264,672256,1662976,
%T 4055040,9764864,23257088,54853632,128253952,297533440,685375488,
%U 1568669696,3569352704,8078229504,18192793600,40785412096,91049951232
%N Binomial transform of positive cubes.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-24,32,-16).
%F a(n) = 2^(n-3)*(n^3+9n^2+18n+8).
%F a(n) = Sum_{k=0..n} C(n, k)*(1+k)^3.
%F O.g.f.: (x-1)*(2*x^2-2*x-1)/(-1+2*x)^4. - _R. J. Mathar_, Apr 02 2008
%F a(n) = A058649(n+1)/n. [_Gary Detlefs_, Nov 26 2011]
%t LinearRecurrence[{8,-24,32,-16},{1,9,44,170},30] (* _Harvey P. Dale_, Jul 30 2023 *)
%o (PARI) a(n) = sum(k=0, n, binomial(n, k)*(1+k)^3); \\ _Michel Marcus_, Oct 13 2016
%Y Cf. A000578, A058645.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jun 13 2003