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A299404
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a(n) = 1 + Sum_{m >= 1} (m + 1)^n/2^(m - 1).
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0
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3, 7, 23, 103, 599, 4327, 37463, 378343, 4366679, 56698087, 817980503, 12981060583, 224732540759, 4214866787047, 85130743763543, 1842265527822823, 42525237455850839, 1042966136233087207, 27084277306054762583, 742412698554627289063, 21421502369955073624919
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OFFSET
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0,1
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LINKS
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Table of n, a(n) for n=0..20.
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FORMULA
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a(n + 1) = 4*A162509(n + 1) + a(n).
a(n) = 2*A007047(n) + 1.
{a(4n - 3), a(4n - 2), a(4n - 1), a(4n)} mod 10 = {7, 3, 3, 9} for n > 0.
floor(log_2(a(n))) = A083652(n).
Lim_{n->infinity} (a(n)^(1/n))/n = 1/(e*log(2)). - Jon E. Schoenfield, Feb 24 2018
a(n)/n! ~ 4 / (log(2))^(n+1). - Vaclav Kotesovec, Apr 17 2018
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MATHEMATICA
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Table[1 + LerchPhi[1/2, -n, 2], {n, 0, 20}] (* Vaclav Kotesovec, Apr 17 2018 *)
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PROG
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(PARI) a(n) = 1+ round(suminf(m=1, (m + 1)^n/2^(m - 1)));
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CROSSREFS
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Cf. A007047, A083652, A162509.
Sequence in context: A100964 A080077 A096318 * A268140 A133788 A120271
Adjacent sequences: A299401 A299402 A299403 * A299405 A299406 A299407
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KEYWORD
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nonn,changed
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AUTHOR
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Joseph Wheat, Feb 20 2018
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STATUS
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approved
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