A120410 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!).
0, 26471025, 11014635520, 1306613597184, 72013536000000, 2320337450970000, 49989108969676800, 785820119347897920, 9577928124440387712, 94609025993497640625, 783056974947287040000, 5572874347584082739200, 34808179069805870776320, 193986366711798174329088
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, 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).
Programs
-
Maple
[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)];
-
Mathematica
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 *)
Formula
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
Extensions
a(0) prepended by Amiram Eldar, Sep 08 2022