A120409 a(n) = n^1*(n+1)^2*(n+2)^3*(n+3)^4*(n+4)^5*(n+5)^6/(1!*2!*3!*4!*5!*6!).
162000, 26471025, 1376829440, 36294822144, 600112800000, 7031325609000, 63117561830400, 457937132487120, 2790771598030416, 14702257341646875, 68449036271616000, 286552568263270400, 1093771338292039680, 3849852478998931776, 12612749124441600000
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (22,-231,1540,-7315,26334,-74613,170544,-319770,497420,-646646, 705432,-646646,497420,-319770,170544,-74613,26334,-7315,1540,-231,22,-1).
Programs
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Maple
[seq(n^1*(n+1)^2*(n+2)^3*(n+3)^4*(n+4)^5*(n+5)^6/(1!*2!*3!*4!*5!*6!),n=1..27)];
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Mathematica
Table[(Times@@Table[(n+k)^(k+1),{k,0,5}])/Times@@(Range[6]!),{n,15}] (* Harvey P. Dale, Jun 07 2022 *) -
Sage
[binomial(n,1)*binomial(n,3)*binomial(n,5)*binomial(n,2)*binomial(n,4)*binomial(n,6) for n in range(6, 19)] # Zerinvary Lajos, May 17 2009
Formula
Sum_{n>=1} 1/a(n) = 789878089*Pi^2/18000 + 64687*Pi^4/150 - 16*Pi^6/21 + 6603436*zeta(3)/25 + 80136*zeta(5) - 56698539425671/64800000. - Amiram Eldar, Sep 08 2022
Extensions
Offset changed from 0 to 1 by Georg Fischer, May 08 2021