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A228290
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a(n) = n^6 + n^5 + n^4 + n^3 + n^2 + n.
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2
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0, 6, 126, 1092, 5460, 19530, 55986, 137256, 299592, 597870, 1111110, 1948716, 3257436, 5229042, 8108730, 12204240, 17895696, 25646166, 36012942, 49659540, 67368420, 90054426, 118778946, 154764792, 199411800, 254313150, 321272406, 402321276, 499738092
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: -6*x*(7*x^4+42*x^3+56*x^2+14*x+1)/(x-1)^7.
a(n) = (n+1)*(n^2+n+1)*a(n-1)/((n-1)*(n^2-3*n+3)) for n>1.
a(1) = 6, else a(n) = (n^7-n)/(n-1).
a(n) = 7*a(n-1) -21*a(n-2) +35*a(n-3) -35*a(n-4) +21*a(n-5) -7*a(n-6) +a(n-7) for n>6, a(0)=0, a(1)=6, a(2)=126, a(3)=1092, a(4)=5460, a(5)=19530, a(6)=55986. - Yosu Yurramendi, Sep 03 2013
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MAPLE
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a:= n-> (1+(1+(1+(1+(1+n)*n)*n)*n)*n)*n:
seq(a(n), n=0..30);
# second Maple program:
a:= proc(n) option remember; `if`(n<2, 6*n,
(n+1)*(n^2+n+1)*a(n-1)/((n-1)*(n^2-3*n+3)))
end:
seq(a(n), n=0..30);
# third Maple program:
a:= n-> `if`(n=1, 6, (n^7-n)/(n-1)):
seq(a(n), n=0..30);
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PROG
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(R)
a <- c(0, 6, 126, 1092, 5460, 19530, 55986)
for(n in (length(a)+1):30) a[n] <- 7*a[n-1] -21*a[n-2] +35*a[n-3] -35*a[n-4] +21*a[n-5] -7*a[n-6] +a[n-7]
a
(PARI) a(n) = n^6 + n^5 + n^4 + n^3 + n^2 + n; \\ Joerg Arndt, Sep 03 2013
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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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