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A083669 Number of ordered quintuples (a,b,c,d,e), -n<= a,b,c,d,e<=n, such that a+b+c+d+e=0. 3
1, 51, 381, 1451, 3951, 8801, 17151, 30381, 50101, 78151, 116601, 167751, 234131, 318501, 423851, 553401, 710601, 899131, 1122901, 1386051, 1692951, 2048201, 2456631, 2923301, 3453501, 4052751, 4726801, 5481631, 6323451, 7258701 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n)= 1+5*n*(n+1)*(23*n^2+23*n+14)/12.

a(n)= integral( (sin((n+1/2)x)/sin(x/2))^5, x=0..Pi)/Pi. - Yalcin Aktar, Dec 03 2011

G.f. ( -1-46*x-136*x^2-46*x^3-x^4 ) / (x-1)^5. - R. J. Mathar, Dec 17 2011

PROG

(PARI) a(n)=115/12*n^4+115/6*n^3+185/12*n^2+35/6*n+1

CROSSREFS

Cf. A003215, A063496.

Sequence in context: A155464 A165087 A152579 * A273189 A222910 A259692

Adjacent sequences:  A083666 A083667 A083668 * A083670 A083671 A083672

KEYWORD

nonn,easy

AUTHOR

Benoit Cloitre, Jun 14 2003

STATUS

approved

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Last modified March 28 22:27 EDT 2017. Contains 284249 sequences.