A120410 - OEIS

%I #13 Sep 08 2022 08:15:17

%S 0,26471025,11014635520,1306613597184,72013536000000,2320337450970000,

%T 49989108969676800,785820119347897920,9577928124440387712,

%U 94609025993497640625,783056974947287040000,5572874347584082739200,34808179069805870776320,193986366711798174329088

%N a(n) = n^1*(n+1)^2*(n+2)^3*(n+3)^4*(n+4)^5*(n+5)^6*(n+6)^7/(1!*2!*3!*4!*5!*6!*7!).

%H <a href="/index/Rec#order_29">Index entries for linear recurrences with constant coefficients</a>, signature (29,-406,3654,-23751,118755,-475020,1560780,-4292145,10015005,-20030010,34597290,-51895935,67863915,-77558760, 77558760,-67863915,51895935,-34597290,20030010,-10015005,4292145,-1560780,475020,-118755,23751,-3654,406,-29,1).

%F Sum_{n>=1} 1/a(n) = 422971791896349857/972000000 - 845737633741*Pi^2/22500 - 230834541*Pi^4/500 - 58492*Pi^6/15 - 18320341039*zeta(3)/1800 - 15501934*zeta(5)/5 - 5040*zeta(7). - _Amiram Eldar_, Sep 08 2022

%p [seq(n^1*(n+1)^2*(n+2)^3*(n+3)^4*(n+4)^5*(n+5)^6*(n+6)^7/(1!*2!*3!*4!*5!*6!*7!),n=1..17)];

%t Table[n*(n+1)^2*(n+2)^3*(n+3)^4*(n+4)^5*(n+5)^6*(n+6)^7/(1!*2!*3!*4!*5!*6!*7!), {n, 0, 10}] (* _Amiram Eldar_, Sep 08 2022 *)

%Y Cf. A090447 A090448 A090449.

%K easy,nonn

%O 0,2

%A _Zerinvary Lajos_, Jul 05 2006

%E a(0) prepended by _Amiram Eldar_, Sep 08 2022