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A352681
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a(n) = [x^n] (3*x + 1)*(1 - sqrt(1 - 4*x))/(2*x).
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1
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1, 4, 5, 11, 29, 84, 258, 825, 2717, 9152, 31382, 109174, 384370, 1366936, 4903140, 17718165, 64442205, 235717800, 866573070, 3200179290, 11865909990, 44158628280, 164881364700, 617507304570, 2319082988274, 8731658843424, 32953192276508, 124635610132460
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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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D-finite with recurrence a(n) = a(n-1)*((14*n + 2)*(2*n - 3))/((7*n - 6)*(n + 1)) for n >= 2.
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MAPLE
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alias(PS = ListTools:-PartialSums):
aList := proc(len) local a, k, P, T; a := 4; P := [1]; T := [1];
for k from 0 to len-1 do T := [op(T), a]; P := PS([op(P), a]); a := P[-1] od;
T end: aList(27);
# Alternative:
a := proc(n) option remember; if n = 0 then 1 elif n = 1 then 4 else
a(n-1)*((14*n + 2)*(2*n - 3))/((7*n - 6)*(n + 1)) fi end: seq(a(n), n = 0..27);
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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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