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A351760
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a(n) = Sum_{1 <= i < j <= n} (i*j)^4.
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0
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0, 0, 16, 1393, 26481, 247731, 1516515, 6978790, 26131686, 83684778, 237014778, 607915231, 1436816095, 3170754405, 6600189141, 13064343516, 24750198748, 45116627556, 79482515700, 135826148445, 225852708445, 366397514791, 581244702423, 903454469346, 1378306878690, 2066986566190
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OFFSET
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0,3
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COMMENTS
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a(n) is the sum of all products of two distinct elements from the set {1^4, ..., n^4}.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
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FORMULA
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a(n) = Sum_{j=2..n} Sum_{i=1..j-1} j^4*i^4.
a(n) = n*(n - 1)*(n + 1)*(2*n - 1)*(2*n + 1)*(9*n^5 + 20*n^4 - 15*n^3 - 50*n^2 + n + 30)/1800.
a(n) = binomial(2*n+2, 5)*(9*n^5 + 20*n^4 - 15*n^3 - 50*n^2 + n + 30)/5!.
G.f.: x^2*(16 + 1217*x + 12038*x^2 + 30415*x^3 + 23364*x^4 + 5263*x^5 + 262*x^6 + x^7)/(1 - x)^11. - Stefano Spezia, Feb 18 2022
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PROG
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(PARI) {a(n) = n*(n-1)*(n+1)*(2*n-1)*(2*n+1)*(9*n^5+20*n^4-15*n^3-50*n^2+n+30)/1800};
(PARI) a(n) = sum(j=2, n, sum(i=1, j-1, i^4*j^4));
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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