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 A027268 a(n) = Sum_{k=0..2n-1} T(n,k) * T(n,k+1), with T given by A026536. 4
 0, 6, 20, 180, 644, 5502, 20292, 174456, 654632, 5673140, 21528000, 187675644, 717800628, 6284986554, 24178479500, 212408191568, 820811282352, 7229648901024, 28037230854096, 247468885359240, 962488105227160, 8510025522045036, 33177800527098040, 293772371437293720 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Table of n, a(n) for n = 1..500 FORMULA a(n) = Sum_{k=0..2n-1} A026536(n,k) * A026536(n,k+1) MATHEMATICA T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n], T[n-1, k-2] +T[n-1, k-1] +T[n-1, k], T[n-1, k-2] +T[n-1, k]] ]]; Table[Sum[T[n, k]*T[n, k+1], {k, 0, 2*n-1}], {n, 40}] (* G. C. Greubel, Apr 12 2022 *) PROG (SageMath) @CachedFunction def T(n, k): # A026536 if k < 0 or n < 0: return 0 elif k == 0 or k == 2*n: return 1 elif k == 1 or k == 2*n-1: return n//2 elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k) return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k) def A027268(n): return sum(T(n, k)*T(n, k+1) for k in (0..2*n-1)) [A027268(n) for n in (1..40)] # G. C. Greubel, Apr 12 2022 CROSSREFS Cf. A026536, A027267, A027269. Sequence in context: A332391 A027148 A095854 * A000388 A347919 A227769 Adjacent sequences: A027265 A027266 A027267 * A027269 A027270 A027271 KEYWORD nonn AUTHOR Clark Kimberling EXTENSIONS More terms from Sean A. Irvine, Oct 26 2019 STATUS approved

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Last modified September 22 00:10 EDT 2023. Contains 365503 sequences. (Running on oeis4.)