A129379 a(n) = sum of sums of all sets of three distinct preceding terms otherwise a(n) = n for n <= 3.

1, 2, 3, 6, 36, 288, 3360, 55440, 1241856, 36427776, 1358235648, 62818398720, 3531789972480, 237336286150656, 18792718657929216, 1732062236305809408, 183865068161693614080, 22273939685873740677120

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..270

Formula

a(n) = (1/2)*(n-2)*(n-3)*Sum_{j=1..n-1} a(j) for n > 3, with a(1) = 1, a(2) = 2, a(3) = 3.

a(n) = A000217(n-3)*A129380(n-1) for n > 3.

From G. C. Greubel, Feb 02 2024: (Start)

a(n) = (6/2^(n-4))*binomial(n-2,2)*|Pochhammer((3+i*sqrt(7))/2, n-4)|^2 for n > 3, otherwise a(n) = n.

a(n) = (3/2^(n-3))*binomial(n-2,2)*Product_{k=0..n-3} (k^2 - k + 2), for n > 3, otherwise a(n) = n.

a(n) = (n-2)*(n^2-7*n+14)/(2*(n-4))*a(n-1), for n > 4, otherwise a(n) = binomial(n, floor(n/2)).

(End)

From Vaclav Kotesovec, Feb 03 2024: (Start)

For n>=4, a(n) = 3 * 2^(3-n) * (n-3) * (n-2) * cosh(sqrt(7)*Pi/2) * Gamma(n - 5/2 - i*sqrt(7)/2) * Gamma(n - 5/2 + i*sqrt(7)/2)/Pi, where i is the imaginary unit.

a(n) ~ 3 * cosh(sqrt(7)*Pi/2) * n^(2*n-4) / (2^(n-4) * exp(2*n)). (End)

Mathematica

a[n_]:= a[n]= If[n<5, Binomial[n, Floor[n/2]], (n-2)*(n^2-7*n+14)*a[n- 1]/(2*(n-4))];
Table[a[n], {n, 40}] (* G. C. Greubel, Feb 02 2024 *)
Round[Flatten[{{1, 2, 3}, Table[3 * 2^(3-n) * (n-3) * (n-2) * Cosh[Sqrt[7]*Pi/2] * Gamma[n - 5/2 - I*Sqrt[7]/2] * Gamma[n - 5/2 + I*Sqrt[7]/2]/Pi, {n, 4, 20}]}]] (* Vaclav Kotesovec, Feb 03 2024 *)

Prog

(Magma)
A129379:= func< n | n le 3 select Binomial(n, Floor(n/2)) else (3/2^(n-3))*Binomial(n-2, 2)*(&*[k^2-k+2: k in [0..n-3]])  >;
[A129379(n): n in [1..30]]; // G. C. Greubel, Feb 02 2024
(SageMath)
def A129379(n): return binomial(n, n//2) if n<4 else 3*binomial(n-2, 2)*product(j^2-j+2 for j in range(n-2))//2^(n-3)
[A129379(n) for n in range(1, 31)] # G. C. Greubel, Feb 02 2024

Crossrefs

Cf. A000217, A083746, A129380.

Sequence in context: A263803 A178175 A351883 * A000308 A299399 A173501

Adjacent sequences: A129376 A129377 A129378 * A129380 A129381 A129382

Keyword

nonn

Author

Reinhard Zumkeller, Apr 14 2007

Status

approved