A090449 - OEIS

%I #19 Sep 08 2022 08:14:46

%S 96,2500,27000,180075,878080,3429216,11340000,32942250,86248800,

%T 207352860,464199736,978193125,1956864000,3741740800,6876627840,

%U 12202737156,20988540000,35103820500,57249238200,91254750895,142462526976,218212500000,328451500000,486489948750

%N Fifth column (m=4) of triangle A090447.

%H T. D. Noe, <a href="/A090449/b090449.txt">Table of n, a(n) for n = 4..1000</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

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

%F 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

%F From _Amiram Eldar_, Sep 08 2022: (Start)

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

%F 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)

%t 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 *)

%Y Cf. A090447.

%K nonn,easy

%O 4,1

%A _Wolfdieter Lang_, Dec 23 2003