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A014827
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a(1)=1, a(n) = 5*a(n-1) + n.
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12
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1, 7, 38, 194, 975, 4881, 24412, 122068, 610349, 3051755, 15258786, 76293942, 381469723, 1907348629, 9536743160, 47683715816, 238418579097, 1192092895503, 5960464477534, 29802322387690, 149011611938471
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (5^(n+1) - 4*n - 5)/16.
G.f.: x/((1-5*x)*(1-x)^2).
a(n) = Sum_{k=0..n} (n-k)*5^k = Sum_{k=0..n} k*5^(n-k). - Paul Barry, Jul 30 2004
a(n) = Sum_{k=0..n} binomial(n+2, k+2)*4^k [Offset 0]. - Paul Barry, Jul 30 2004
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MAPLE
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a:=n->sum((5^(n-j)-1^(n-j))/4, j=0..n): seq(a(n), n=1..21); # Zerinvary Lajos, Jan 04 2007
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MATHEMATICA
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PROG
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(Sage) [(gaussian_binomial(n, 1, 5)-n)/4 for n in range(2, 23)] # Zerinvary Lajos, May 29 2009
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CROSSREFS
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Cf. A016218, A016208, A000392, A000225, A003462, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A016256.
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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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