A337992 a(n) = Sum_{k=0..n} (n+1)*2^(n+k)*hypergeom([-n, k-n+1], [2], 1/2). Row sums of A337617.
1, 10, 70, 448, 2786, 17140, 104938, 640720, 3904738, 23762140, 144429770, 876959896, 5319995474, 32247562084, 195332428970, 1182430057888, 7153644523970, 43256701913260, 261441118446154, 1579452451096168, 9538212470700466, 57579647214814900, 347476026056519210
Offset: 0
Keywords
Crossrefs
Cf. A337617.
Programs
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Mathematica
a[n_] := Sum[If[n==k, 2^n*(2^(n + 1) - 1), 2^(2*k + 1)*Sum[(-1)^j*2^(n - k - j)*Binomial[n + 1, j]*Binomial[2*n - j - k, n],{j, 0, n-k}]],{k, 0, n}]; Flatten[Table[a[n], {n, 0, 22}]] (* Detlef Meya, Jan 09 2024 *)
Formula
a(n) = Sum_{k=0..n} (if (n = k) then 2^n*(2^(n + 1) - 1) else 2^(2*k + 1)*Sum(j, 0..n - k) (-1)^j*2^(n - k - j)*binomial(n + 1, j)*binomial(2*n - j - k, n)). - _Detlef Meya, Jan 09 2024
a(n) ~ 2^n * 3^(n+1). - Vaclav Kotesovec, Jan 10 2024