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%I #17 Sep 08 2022 08:45:41
%S 1,7,28,86,227,545,1230,2664,5613,11611,23728,48106,97031,195077,
%T 391394,784284,1570353,3142815,6288100,12579070,25161451,50326697,
%U 100657718,201320336,402646197,805298595
%N G.f. of the z^1 coefficients of the FP1 in the second column of the A156921 matrix.
%C Antidiagonal sums of the convolution array A213582. - _Clark Kimberling_, Jun 19 2012
%H G. C. Greubel, <a href="/A156928/b156928.txt">Table of n, a(n) for n = 2..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-14,16,-9,2).
%F a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) + 2.
%F a(n) = 6*a(n-1) - 14*a(n-2) + 16*a(n-3) - 9*a(n-4) + 2*a(n-5).
%F a(n) = (9*2^(n+2) - (2*n^3 + 9*n^2 + 25*n + 36))/6.
%F G.f.: GF3(z;m=1) = z^2*(1+z)/((1-z)^4*(1-2*z)).
%F a(n) = Sum_{k=1..n+1} Sum_{i=1..n+1} (k-1)^2 * C(n-k+1,i). - _Wesley Ivan Hurt_, Sep 22 2017
%F E.g.f.: (36*exp(2*x) - (36 + 36*x + 15*x^2 + 2*x^3)*exp(x))/6. - _G. C. Greubel_, Jul 08 2019
%t Table[(9*2^(n+2) -(2*n^3+9*n^2+25*n+36))/6, {n, 2, 40}] (* _Michael De Vlieger_, Sep 23 2017 *)
%o (PARI) vector(40, n, n++; (9*2^(n+2) -(2*n^3+9*n^2+25*n+36))/6) \\ _G. C. Greubel_, Jul 08 2019
%o (Magma) [(9*2^(n+2) -(2*n^3+9*n^2+25*n+36))/6: n in [2..40]]; // _G. C. Greubel_, Jul 08 2019
%o (Sage) [(9*2^(n+2) -(2*n^3+9*n^2+25*n+36))/6 for n in (2..40)] # _G. C. Greubel_, Jul 08 2019
%o (GAP) List([2..40], n-> (9*2^(n+2) -(2*n^3+9*n^2+25*n+36))/6) # _G. C. Greubel_, Jul 08 2019
%Y Cf. A156927.
%Y Equals second column of A156921.
%Y Other columns A156929, A156930, A156931.
%K easy,nonn
%O 2,2
%A _Johannes W. Meijer_, Feb 20 2009
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