Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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