The Collaborative International Dictionary of English v.0.48:

Invitation \In`vi*ta"tion\, n. [L. invitatio: cf. F. invitation.
   See Invite.]
   [1913 Webster]
   1. The act of inviting; solicitation; the requesting of a
      person's company; as, an invitation to a party, to a
      dinner, or to visit a friend.
      [1913 Webster]

   2. A document written or printed, or spoken words, conveying
      the message by which one is invited.
      [1913 Webster]

   3. Allurement; enticement. [R.]
      [1913 Webster]

            She gives the leer of invitation.     --Shak.
      [1913 Webster]

WordNet (r) 3.0 (2006):

invitation
    n 1: a request (spoken or written) to participate or be present
         or take part in something; "an invitation to lunch"; "she
         threw the invitation away"
    2: a tempting allurement; "she was an invitation to trouble"

Moby Thesaurus II by Grady Ward, 1.0:

85 Moby Thesaurus words for "invitation":
   advance, agacerie, allure, allurement, appeal, approach,
   asking price, attraction, attractiveness, bait, beguilement,
   beguiling, bewitchery, bewitchment, bid, biddance, bidding,
   blandishment, bribe, cajolery, call, calling, captivation, carrot,
   charisma, charm, charmingness, come-hither, draw, enchantment,
   encouragement, engraved invitation, enthrallment, enticement,
   entrapment, fascination, feeler, fillip, flirtation,
   forbidden fruit, glamour, incentive, incitement, inducement,
   interest, inveiglement, invite, lure, magnetism, offer, offering,
   overture, payment, percentage, persuasive, preliminary approach,
   presentation, proffer, profit, proposition, provocation, pull,
   request, reward, seducement, seduction, seductiveness, sex appeal,
   snaring, stimulation, stimulative, stimulus, submission,
   suggestion, summons, sweetener, sweetening, tantalization,
   temptation, tentative approach, whet, winning ways, winsomeness,
   witchery, wooing