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%I #24 Mar 22 2023 08:13:43
%S 0,1,130,2574,25904,183200,1040112,5076400,22171648,88915968,
%T 333209600,1181548544,4001402880,13033885696,41061830656,125666611200,
%U 374947708928,1093874155520,3128047828992,8785866391552,24280799641600,66124498599936,177683966197760
%N Binomial transform of n^7.
%C The binomial transforms of n, n^2, n^3, n^4, n^5, n^6 are A001787, A001788, A058645, A058649, A059338, A056468 respectively.
%H G. C. Greubel, <a href="/A084641/b084641.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (16,-112,448,-1120,1792,-1792,1024,-256).
%F a(n) = n^2*(n^5 + 21*n^4 + 105*n^3 + 35*n^2 - 210*n + 112)*2^(n-7).
%F a(n) = Sum_{k=0..n} C(n, k)*k^7.
%F G.f.: x*(1+114*x+606*x^2-1168*x^3-96*x^4+816*x^5-272*x^6)/(1-2*x)^8. - _Colin Barker_, Sep 20 2012
%t LinearRecurrence[{16,-112,448,-1120,1792,-1792,1024,-256}, {0,1,130, 2574,25904,183200,1040112,5076400}, 41] (* _Amiram Eldar_, Nov 26 2021 *)
%o (Magma) [n^2*(n^5+21*n^4+105*n^3+35*n^2-210*n+112)*2^(n-7): n in [0..40]]; // _G. C. Greubel_, Mar 20 2023
%o (SageMath) [n^2*(n^5+21*n^4+105*n^3+35*n^2-210*n+112)*2^(n-7) for n in range(41)] # _G. C. Greubel_, Mar 20 2023
%Y Cf. A001015, A001787, A001788, A058645, A058649, A059338, A056468.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Jun 08 2003
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