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A249060 Column 1 of the triangular array at A249057. 3
1, 4, 5, 24, 35, 192, 315, 1920, 3465, 23040, 45045, 322560, 675675, 5160960, 11486475, 92897280, 218243025, 1857945600, 4583103525, 40874803200, 105411381075, 980995276800, 2635284526875, 25505877196800, 71152682225625, 714164561510400, 2063427784543125 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For n > 2, if n is even, a(n)/[(n+1)*(n-1)*(n-3)*...*7*5] = n + 3 and if n is odd, a(n)/[(n+1)*(n-1)*(n-3)*...*6*4] = n + 3. - Derek Orr, Oct 21 2014

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..100

FORMULA

a(2*n) = (2*n+3)*(2*n+1)!!/3, for n > 0. - Derek Orr, Oct 21 2014

a(2*n+1) = (n+2)!*2^(n+1), for n > 0. - Derek Orr, Oct 21 2014

a(n) = gcd_2((n+3)!,(n+3)!!), where gcd_2(b,c) denotes the second-largest common divisor of non-coprime integers b and c, as defined in A309491. - Lechoslaw Ratajczak, Apr 15 2021

EXAMPLE

First 3 rows from A249057:

1

4    1

5    4    1,

so that a(0) = 1, a(1) = 4, a(2) = 5.

MATHEMATICA

z = 30; p[x_, n_] := x + (n + 2)/p[x, n - 1]; p[x_, 1] = 1;

t = Table[Factor[p[x, n]], {n, 1, z}];

u = Numerator[t]; v1 = Flatten[CoefficientList[u, x]]; (* A249057  *)

v2 = u /. x -> 1  (* A249059 *)

v3 = u /. x -> 0  (* A249060 *)

CROSSREFS

Cf. A249057, A249060.

Sequence in context: A042123 A041531 A089499 * A042601 A219515 A248246

Adjacent sequences:  A249057 A249058 A249059 * A249061 A249062 A249063

KEYWORD

nonn,easy,changed

AUTHOR

Clark Kimberling, Oct 20 2014

STATUS

approved

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Last modified May 15 20:23 EDT 2021. Contains 343920 sequences. (Running on oeis4.)