cp's OEIS Frontend

A026965 a(n) = Sum_{k=0..n} (k+1) * A026626(n,k).

%I A026965 #18 Feb 21 2025 22:42:22
%S A026965 1,3,10,25,66,154,360,810,1810,3982,8700,18850,40614,87030,185680,
%T A026965 394570,835578,1763998,3713700,7798770,16340302,34166086,71303160,
%U A026965 148548250,308980386,641728494,1330992460,2757055810,5704253430
%N A026965 a(n) = Sum_{k=0..n} (k+1) * A026626(n,k).
%H A026965 G. C. Greubel, <a href="/A026965/b026965.txt">Table of n, a(n) for n = 0..1000</a>
%H A026965 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-8,7,4,-4).
%F A026965 G.f.: (1-x-x^3+3*x^4-5*x^5-2*x^6+3*x^7)/((1-x)^2*(1+x)^2*(1-2*x)^2). - _Colin Barker_, Apr 26 2015
%F A026965 From _G. C. Greubel_, Jun 23 2024: (Start)
%F A026965 a(n) = (1/6)*(n+2)*(17*2^(n-2) - 3 + (-1)^n) + (1/4)*([n=0] + 3*[n=1]).
%F A026965 a(n) = ( n*(n+2)*a(n-1) + 2*(n+1)*(n+2)*a(n-2) + n*(n+1)*(n+2) )/(n*(n + 1)), with a(0) = 1, a(1) = 3, a(2) = 10, a(3) = 25.
%F A026965 E.g.f.: (1/12)*( 17*(1+x)*exp(2*x) - 6*(2+x)*exp(x) + 2*(2-x)*exp(-x) + 3*(1+3*x) ). (End)
%t A026965 Table[(n+2)*(17*2^(n-2) -3 +(-1)^n)/6 +(1/4)*(Boole[n==0] +3*Boole[n== 1]), {n,0,50}] (* _G. C. Greubel_, Jun 23 2024 *)
%o A026965 (Magma) [n le 1 select 2*n+1 else (n+2)*(17*2^(n-2) -3 +(-1)^n)/6: n in [0..40]]; // _G. C. Greubel_, Jun 23 2024
%o A026965 (SageMath) [(n+2)*(17*2^(n-2) -3 +(-1)^n)/6 + (1/4)*(int(n==0) + 3*int(n==1)) for n in range(41)] # _G. C. Greubel_, Jun 23 2024
%Y A026965 Cf. A026626, A026627, A026628, A026629, A026630, A026631, A026632.
%Y A026965 Cf. A026633, A026634, A026635, A026636, A026961, A026962, A026963.
%Y A026965 Cf. A026964.
%K A026965 nonn,easy
%O A026965 0,2
%A A026965 _Clark Kimberling_