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 A101102 Fifth partial sums of cubes (A000578). 15
 1, 13, 82, 354, 1200, 3432, 8646, 19734, 41613, 82225, 153868, 274924, 472056, 782952, 1259700, 1972884, 3016497, 4513773, 6624046, 9550750, 13550680, 18944640, 26129610, 35592570, 47926125, 63846081, 84211128, 110044792, 142559824, 183185200, 233595912 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). FORMULA a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(10 + 3*n*(n+5))/20160. This sequence could be obtained from the general formula a(n) = n*(n+1)*(n+2)*(n+3)*...*(n+k)*(n*(n+k) + (k-1)*k/6)/((k+3)!/6) at k=5. - Alexander R. Povolotsky, May 17 2008 G.f.: x*(x^2+4*x+1) / (1-x)^9. - Colin Barker, Apr 23 2015 MATHEMATICA Table[binomial[n+5, 6]*(3*n^2+15*n+10)/28, {n, 1, 30}] (* G. C. Greubel, Dec 01 2018 *) PROG (PARI) a(n)=sum(t=1, n, sum(s=1, t, sum(l=1, s, sum(j=1, l, sum(m=1, j, sum(i=m*(m+1)/2-m+1, m*(m+1)/2, (2*i-1))))))) \\ Alexander R. Povolotsky, May 17 2008 (PARI) Vec(-x*(x^2+4*x+1)/(x-1)^9 + O(x^100)) \\ Colin Barker, Apr 23 2015 (PARI) a(n) = binomial(n+5, 6)*(3*n^2+15*n+10)/28 \\ Charles R Greathouse IV, Apr 23 2015 (MAGMA) [Binomial(n+5, 6)*(3*n^2+15*n+10)/28: n in [1..30]]; // G. C. Greubel, Dec 01 2018 (Sage) [binomial(n+5, 6)*(3*n^2+15*n+10)/28 for n in  (1..30)] # G. C. Greubel, Dec 01 2018 CROSSREFS Cf. A000537, A024166, A101094. Partial sums of A101097. Sequence in context: A241696 A052255 A082203 * A213572 A142085 A163688 Adjacent sequences:  A101099 A101100 A101101 * A101103 A101104 A101105 KEYWORD easy,nonn AUTHOR Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004 EXTENSIONS Edited by Ralf Stephan, Dec 16 2004 STATUS approved

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Last modified August 22 00:43 EDT 2019. Contains 326169 sequences. (Running on oeis4.)