A090449 Fifth column (m=4) of triangle A090447.

96, 2500, 27000, 180075, 878080, 3429216, 11340000, 32942250, 86248800, 207352860, 464199736, 978193125, 1956864000, 3741740800, 6876627840, 12202737156, 20988540000, 35103820500, 57249238200, 91254750895, 142462526976, 218212500000, 328451500000, 486489948750

Offset

4,1

Links

T. D. Noe, Table of n, a(n) for n = 4..1000

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

a(n)= A090447(n, 4)= (n^4*(n-1)^3*(n-2)^2*(n-3)^1)/(1!*2!*3!*4!), n>=4.

G.f.: -x^4*(x^6+109*x^5+1435*x^4+4735*x^3+4780*x^2+1444*x+96)/(x-1)^11. - Colin Barker, Jan 21 2013

From Amiram Eldar, Sep 08 2022: (Start)

Sum_{n>=4} 1/a(n) = 700*Pi^2/9 + 4*Pi^4/15 - 40*zeta(3) - 20129/27.

Sum_{n>=4} (-1)^n/a(n) = 30311/27 - 26*Pi^2/9 - 7*Pi^4/30 - 11008*log(2)/9 - 186*zeta(3). (End)

Mathematica

LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {96, 2500, 27000, 180075, 878080, 3429216, 11340000, 32942250, 86248800, 207352860, 464199736}, 40] (* Harvey P. Dale, Apr 10 2018 *)

Crossrefs

Cf. A090447.

Sequence in context: A268636 A233153 A204624 * A336677 A233709 A268901

Adjacent sequences: A090446 A090447 A090448 * A090450 A090451 A090452

Keyword

nonn,easy

Author

Wolfdieter Lang, Dec 23 2003

Status

approved