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

Author

Wolfdieter Lang, Dec 23 2003

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A090447.

Programs

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 *)

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)