%I A143314
%S A143314 0,0,0,0,40,1844,41584,611340,6588116,55482100,380126920,2177910310,
%T A143314 10644616240,45049914588,167011924492,547315800984,1597026077496,
%U A143314 4173458163098,9813490226056,20841357619302,40096048882028
%N A143314 Number of hands of n cards containing a straight flush (for n=1 to 52).
%C A143314 With a regular deck of 52 playing cards (4 suits of 13 cards: 23456789TJQKA) 
               a "straight flush" consists of 5 cards of the same suit with consecutive 
               values. The ace (A) is considered to come either before the deuce 
               (2) or after the king (K).
%C A143314 The first terms of the sequence are zero because there are no straight 
               flushes in a hand of fewer than 5 cards.
%H A143314 Gerard P. Michon (g.michon(AT)att.net), Aug 06 2008, <a href="b143314.txt">
               Table of n, a(n) for n = 1..52</a>
%H A143314 G. P. Michon, <a href="http://www.numericana.com/answer/counting.htm#stud26">
               q-Card Poker</a>.
%F A143314 The generating function is a polynomial: (1+x)^52-[(1+x)^13-x^5(1+x)(10+61x+156x^2+215x^3+169x^4+65x^5+12x^6+\
               x^7)]^4
%e A143314 a(5)=40 because each suit allows 10 straight flushes (2 of which contain 
               an ace).
%e A143314 a(44)=752538149=C(52,44)-1 because there's only one way to avoid a straight 
               flush with 44 cards (namely, 2346789JQKA in every suit).
%e A143314 a(45)=133784560=C(52,45) because every hand of 45 cards (or more) includes 
               a straight flush.
%e A143314 a(52)=1 decause there's only one "hand" of 52 cards.
%Y A143314 Cf. A002761, A002806, A002834, A002879.
%Y A143314 Sequence in context: A140702 A145294 A147520 this_sequence A060056 A140729 
               A003741
%Y A143314 Adjacent sequences: A143311 A143312 A143313 this_sequence A143315 A143316 
               A143317
%K A143314 fini,full,nonn
%O A143314 1,5
%A A143314 Gerard P. Michon (g.michon(AT)att.net), Aug 06 2008