A299404 a(n) = 1 + Sum_{m >= 1} (m + 1)^n/2^(m - 1).

3, 7, 23, 103, 599, 4327, 37463, 378343, 4366679, 56698087, 817980503, 12981060583, 224732540759, 4214866787047, 85130743763543, 1842265527822823, 42525237455850839, 1042966136233087207, 27084277306054762583, 742412698554627289063, 21421502369955073624919

Offset

0,1

Links

Table of n, a(n) for n=0..20.

Formula

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

Mathematica

Table[1 + LerchPhi[1/2, -n, 2], {n, 0, 20}] (* Vaclav Kotesovec, Apr 17 2018 *)

Prog

(PARI) a(n) = 1+ round(suminf(m=1, (m + 1)^n/2^(m - 1)));

Crossrefs

Cf. A007047, A083652, A162509.

Sequence in context: A100964 A080077 A096318 * A268140 A133788 A120271

Adjacent sequences: A299401 A299402 A299403 * A299405 A299406 A299407

Keyword

nonn

Author

Joseph Wheat, Feb 20 2018

Status

approved