A328000 -id:A328000 - cp's OEIS frontend

A327999 a(n) = Sum_{k=0..2n}(k!(2n - k)!)/(floor(k/2)!floor((2n - k)/2)!)^2.

1, 5, 28, 160, 896, 4864, 25600, 131072, 655360, 3211264, 15466496, 73400320, 343932928, 1593835520, 7314866176, 33285996544, 150323855360, 674309865472, 3006477107200, 13331578486784, 58823872086016, 258385232527360, 1130297953353728, 4925812092436480

Offset: 0

Peter Luschny, Oct 01 2019

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (12,-48,64).

Even bisection of A328000.

LinearRecurrence[{12, -48, 64}, {1, 5, 28}, 24] (* Michael De Vlieger, Feb 07 2020 *)

Vec((1 - 7*x + 16*x^2) / (1 - 4*x)^3 + O(x^25)) \\ Colin Barker, Feb 05 2020

apply( {A327999(n)=(n^2+n+8)<<(2*n-3)}, [0..25]) \\ M. F. Hasler, Feb 07 2020

a(n) = 4^n*(n^2 + n + 8)/8.
a(n) = [x^n] (-16*x^2 + 7*x - 1)/(4*x - 1)^3.
a(n) = n! [x^n] exp(4*x)*(2*x^2 + x + 1).
a(n) = a(n-1)*4*(8 + n + n^2)/(8 - n + n^2).
a(n) = A328000(2*n).
From Colin Barker, Feb 05 2020: (Start)
a(n) = 12*a(n-1) - 48*a(n-2) + 64*a(n-3) for n>2.
a(n) = 2^(2*n - 3)*(8 + n + n^2).
(End)

A328001 T(n, k) = k!(n-k)!/(floor(k/2)!floor((n-k)/2)!)^2. Triangle read by rows, 0 <= k <= n.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 6, 2, 2, 6, 6, 6, 4, 6, 6, 30, 6, 12, 12, 6, 30, 20, 30, 12, 36, 12, 30, 20, 140, 20, 60, 36, 36, 60, 20, 140, 70, 140, 40, 180, 36, 180, 40, 140, 70, 630, 70, 280, 120, 180, 180, 120, 280, 70, 630, 252, 630, 140, 840, 120, 900, 120, 840, 140, 630, 252

Offset: 0

Peter Luschny, Oct 01 2019

			                               1;
                              1, 1;
                            2, 1, 2;
                           6, 2, 2, 6;
                         6, 6, 4, 6, 6;
                      30, 6, 12, 12, 6, 30;
                   20, 30, 12, 36, 12, 30, 20;
                140, 20, 60, 36, 36, 60, 20, 140;
             70, 140, 40, 180, 36, 180, 40, 140, 70;
         630, 70, 280, 120, 180, 180, 120, 280, 70, 630;

Row sums in A328000. Central column in A327998.

Cf. A056040.

T := (n, k) -> k!*(n-k)!/(iquo(k, 2)!*iquo(n-k, 2)!)^2:
seq(seq(T(n,k), k=0..n), n=0..10);

T(n, k) = s(k)*s(n-k) where s(n) = A056040(n).

cp's OEIS Frontend

A327999 a(n) = Sum_{k=0..2n}(k!(2n - k)!)/(floor(k/2)!floor((2n - k)/2)!)^2.

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Formula

A328001 T(n, k) = k!(n-k)!/(floor(k/2)!floor((n-k)/2)!)^2. Triangle read by rows, 0 <= k <= n.

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Maple

Formula

cp's OEIS Frontend

A327999 a(n) = Sum_{k=0..2n}(k!*(2n - k)!)/(floor(k/2)!*floor((2n - k)/2)!)^2.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

A328001 T(n, k) = k!*(n-k)!/(floor(k/2)!*floor((n-k)/2)!)^2. Triangle read by rows, 0 <= k <= n.

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

Formula

A327999 a(n) = Sum_{k=0..2n}(k!(2n - k)!)/(floor(k/2)!floor((2n - k)/2)!)^2.

A328001 T(n, k) = k!(n-k)!/(floor(k/2)!floor((n-k)/2)!)^2. Triangle read by rows, 0 <= k <= n.