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

0,2

Links

Table of n, a(n) for n=0..22.

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

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 *)

Crossrefs

Cf. A337617.

Sequence in context: A125347 A005465 A229702 * A257114 A037600 A037705

Adjacent sequences: A337989 A337990 A337991 * A337993 A337994 A337995

Keyword

nonn

Author

Peter Luschny, Oct 19 2020

Status

approved