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%I A073374 #14 Sep 30 2022 01:45:33
%S A073374 1,5,25,95,340,1106,3430,10130,28915,80035,216143,571225,1482110,
%T A073374 3783640,9522740,23665300,58149845,141435985,340854645,814589475,
%U A073374 1931900376,4549699950,10645737330,24761578470
%N A073374 Fourth convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself.
%H A073374 G. C. Greubel, <a href="/A073374/b073374.txt">Table of n, a(n) for n = 0..1000</a>
%H A073374 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (5,0,-30,15,81,-30,-120,0,80,32).
%F A073374 a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A001045(k+1) and c(k) = A073373(k).
%F A073374 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+4, 4) * binomial(n-k, k) * 2^k.
%F A073374 a(n) = (5*(2968 +1974*n +411*n^2 +27*n^3)*(n+1)*U(n+1) + 2*(9412 +6099*n +1248*n^2 +81*n^3)*(n+2)*U(n))/(4!*3^7) with U(n) = A001045(n+1), n>=0.
%F A073374 G.f.: 1/(1-(1+2*x)*x)^5 = 1/((1+x)*(1-2*x))^5.
%F A073374 E.g.f.: (1/157464)*(512*(263 + 1104*x + 1026*x^2 + 306*x^3 + 27*x^4)*exp(2*x) + (22808 - 24432*x + 7344*x^2 - 792*x^3 + 27*x^4)*exp(-x)). - _G. C. Greubel_, Sep 29 2022
%t A073374 Table[(2^(n+5)*(4208+5790*n+2565*n^2+450*n^3+27*n^4) + (-1)^n*(22808+18510*n+ 5265*n^2+630*n^3+27*n^4))/157464, {n,0,40}] (* _G. C. Greubel_, Sep 29 2022 *)
%o A073374 (Magma) [(2^(n+5)*(4208+5790*n+2565*n^2+450*n^3+27*n^4) + (-1)^n*(22808+18510*n+ 5265*n^2+630*n^3+27*n^4))/157464: n in [0..40]]; // _G. C. Greubel_, Sep 29 2022
%o A073374 (SageMath)
%o A073374 def A073374(n): return (2^(n+5)*(4208+5790*n+2565*n^2+450*n^3+27*n^4) + (-1)^n*(22808+18510*n+ 5265*n^2+630*n^3+27*n^4))/157464
%o A073374 [A073374(n) for n in range(40)] # _G. C. Greubel_, Sep 29 2022
%Y A073374 Fifth (m=4) column of triangle A073370.
%Y A073374 Cf. A001045, A073373.
%K A073374 nonn,easy
%O A073374 0,2
%A A073374 _Wolfdieter Lang_, Aug 02 2002

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