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 Closed Closure (Posted on 2011-04-28)
Determine, with proof, the closed form of following expression in terms of n

Σj=1 to n  j2*(j+1)*(nCj)

 See The Solution Submitted by K Sengupta No Rating

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 here are some numbers in case they help | Comment 1 of 3

Some values are listed below, in case that helps:

`  5   for N=1 to 40  6    Tot=0 10    for J=1 to N 20     Term=J*J*(J+1)*combi(N,J) 30     Tot=Tot+Term 40    next J 45    print N,Tot 50   next N n       sum1       22       163       784       3045       10406       32647       96328       271369       7372810      19456011      50124812      126566413      314163214      768409615      1855488016      4430233617      10472652818      24536678419      57029427220      131596288021      301675315222      687446425623      1557974220824      3513149030425      7885291520026      17622787686427      39228486451228      86999931289629      192280317132830      423591149568031      930343603404832      2037532485222433      4450445112115234      9696318167449635      21075404521472036      45705323977113637      98907942866124838      213607621486182439      460434238026547240      9906599766261760 `
`The terms are broken down below:`
` 5   for N=1 to 9 6    Tot=0:print N,10    for J=1 to N20     Term=J*J*(J+1)*combi(N,J):print Term;30     Tot=Tot+Term40    next J45    print ":";Tot50   next N   n       terms and total1       2 : 22       4  12 : 163       6  36  36 : 784       8  72  144  80 : 3045       10  120  360  400  150 : 10406       12  180  720  1200  900  252 : 32647       14  252  1260  2800  3150  1764  392 : 96328       16  336  2016  5600  8400  7056  3136  576 : 271369       18  432  3024  10080  18900  21168  14112  5184  810 : 73728`

 Posted by Charlie on 2011-04-28 11:44:18

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