cp's OEIS Frontend

A027075 a(n) = Sum_{k=0..2n} (k+1) * A027052(n, k).

%I A027075 #13 Nov 07 2019 08:28:38
%S A027075 1,4,17,58,199,682,2301,7654,25145,81740,263407,842720,2679935,
%T A027075 8479378,26713555,83847748,262335577,818473148,2547289679,7910433568,
%U A027075 24517303535,75854736178,234317624167,722776320072,2226565995913
%N A027075 a(n) = Sum_{k=0..2n} (k+1) * A027052(n, k).
%H A027075 G. C. Greubel, <a href="/A027075/b027075.txt">Table of n, a(n) for n = 0..1000</a>
%p A027075 T:= proc(n, k) option remember;
%p A027075       if k<0 or k>2*n then 0
%p A027075     elif k=0 or k=2 or k=2*n then 1
%p A027075     elif k=1 then 0
%p A027075     else add(T(n-1, k-j), j=1..3)
%p A027075       fi
%p A027075     end:
%p A027075 seq( add((k+1)*T(n,k), k=0..2*n), n=0..30); # _G. C. Greubel_, Nov 06 2019
%t A027075 T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2 || k==2*n, 1, If[k==1, 0, Sum[T[n-1, k-j], {j, 3}]]]]; Table[Sum[(k+1)*T[n,k], {k, 0, 2*n}], {n,0,30}] (* _G. C. Greubel_, Nov 06 2019 *)
%o A027075 (Sage)
%o A027075 @CachedFunction
%o A027075 def T(n, k):
%o A027075     if (k<0 or k>2*n): return 0
%o A027075     elif (k==0 or k==2 or k==2*n): return 1
%o A027075     elif (k==1): return 0
%o A027075     else: return sum(T(n-1, k-j) for j in (1..3))
%o A027075 [sum((k+1)*T(n,k) for k in (0..2*n)) for n in (0..30)] # _G. C. Greubel_, Nov 06 2019
%K A027075 nonn
%O A027075 0,2
%A A027075 _Clark Kimberling_