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A101090
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Third partial sums of fourth powers (A000583).
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10
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1, 19, 135, 605, 2054, 5778, 14178, 31350, 63855, 121693, 219505, 378027, 625820, 1001300, 1555092, 2352732, 3477741, 5035095, 7155115, 9997801, 13757634, 18668870, 25011350, 33116850, 43375995, 56245761, 72257589, 92026135
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OFFSET
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1,2
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COMMENTS
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In general, the r-th successive summation of the fourth powers from 1 to n = (2*n+r)*(12*n^2+12*n*r+r^2-5*r)*(r+n)!/((r+4)!*(n-1)!). Here r = 3. - Gary Detlefs, Mar 01 2013
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LINKS
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FORMULA
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a(n) = (n*(1+n)*(2+n)*(3+n)*(3+2*n)*(-1+2*n*(3+n)))/840.
G.f.: x*(1+x)*(1+10*x+x^2)/(1-x)^8. [Colin Barker, Apr 04 2012]
a(n)= (2*n+3)*(12*n^2+36*n-6)*(n+3)!/(5040*(n-1)!), n>0 - Gary Detlefs, Mar 01 2013
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 14 2004
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EXTENSIONS
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STATUS
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approved
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