  The census of exoplanets is incomplete for orbital distances larger than 1
AU. Here, we present 41 long-period planet candidates in 38 systems identified
by Planet Hunters based on Kepler archival data (Q0-Q17). Among them, 17
exhibit only one transit, 14 have two visible transits and 10 have more than
three visible transits. For planet candidates with only one visible transit, we
estimate their orbital periods based on transit duration and host star
properties. The majority of the planet candidates in this work (75%) have
orbital periods that correspond to distances of 1-3 AU from their host stars.
We conduct follow-up imaging and spectroscopic observations to validate and
characterize planet host stars. In total, we obtain adaptive optics images for
33 stars to search for possible blending sources. Six stars have stellar
companions within 4". We obtain high-resolution spectra for 6 stars to
determine their physical properties. Stellar properties for other stars are
obtained from the NASA Exoplanet Archive and the Kepler Stellar Catalog by
Huber et al. (2014). We validate 7 planet candidates that have planet
confidence over 0.997 (3-{\sigma} level). These validated planets include 3
single-transit planets (KIC-3558849b, KIC-5951458b, and KIC-8540376c), 3
planets with double transits (KIC-8540376b, KIC-9663113b, and KIC-10525077b),
and 1 planet with 4 transits (KIC-5437945b). This work provides assessment
regarding the existence of planets at wide separations and the associated false
positive rate for transiting observation (17%-33%). More than half of the
long-period planets with at least three transits in this paper exhibit transit
timing variations up to 41 hours, which suggest additional components that
dynamically interact with the transiting planet candidates. The nature of these
components can be determined by follow-up radial velocity and transit
observations.
