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A013776
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a(n) = 2^(4*n+1).
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10
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2, 32, 512, 8192, 131072, 2097152, 33554432, 536870912, 8589934592, 137438953472, 2199023255552, 35184372088832, 562949953421312, 9007199254740992, 144115188075855872, 2305843009213693952
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OFFSET
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0,1
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COMMENTS
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a(n) ~ -Pi*E(2*n)/B(2*n), E(n) Euler number, B(n) Bernoulli number. - Peter Luschny, Oct 28 2012
Equivalently, powers of 2 with final digit 2. - Muniru A Asiru, Mar 15 2019
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LINKS
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FORMULA
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a(n) = 16*a(n-1), n > 0, a(0) = 2.
G.f.: 2/(1 - 16*x). (End)
a(n) = Sum_{k = 0..n} binomial(2*k,k)*binomial(4*n + 2 - 2*k, 2*n + 1 - k).
a(n) = Sum_{k = 0..2*n} binomial(4*n + 2, 2*k + 1) = A004171(2*n). - Peter Bala, Nov 25 2016
Sum_{n>=0} 1/a(n) = 8/15.
Sum_{n>=0} (-1)^n/a(n) = 8/17. (End)
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EXAMPLE
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G.f. = 2 + 32*x + 512*x^2 + 8192*x^3 + 131072*x^4 + 2097152*x^5 + ...
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MAPLE
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MATHEMATICA
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PROG
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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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EXTENSIONS
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STATUS
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approved
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