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 A309777 Number of ways of being dealt an n-point Bridge hand. 0
 1, 4, 10, 24, 51, 96, 170, 284, 445, 664, 952, 1304, 1716, 2184, 2680, 3176, 3650, 4064, 4380, 4584, 4658, 4584, 4380, 4064, 3650, 3176, 2680, 2184, 1716, 1304, 952, 664, 439, 268, 148, 64, 25, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Points are counted in the standard (Milton Work) way, Ace=4, King=3, Queen=2, Jack=1, all other cards = 0. The first term a(0) then is the number of ways of being dealt a "Yarborough" (a hand with 0 points). That consists of 13 cards with 0 Aces, 0 Kings, 0 Queens and 0 Jacks which, all other cards being considered as indistinguishable, can be dealt in 1 way. The final term, a(37), represents a 37-point hand consisting of 4 Aces, 4 Kings, 4 Queens and 1 Jack. This can be dealt in 4 ways (the Jack is of any one of the four suits Clubs, Diamonds, Hearts, Spades). May you be dealt many of them (but not against me). The sequence would of course be symmetric, and sum to 2^16 except for the restriction to 13 cards. LINKS FORMULA a(n) = [y^n][x^13]((Product_{k=1..4} 1 + x*y^k)^4/(1-x)). - Andrew Howroyd, Aug 23 2019 PROG (PARI) Vecrev(polcoef(prod(k=1, 4, (1 + x*y^k + O(x*x^13))^4)/(1-x), 13)) \\ Andrew Howroyd, Aug 22 2019 CROSSREFS Sequence in context: A001979 A209970 A211392 * A128516 A022569 A093831 Adjacent sequences:  A309774 A309775 A309776 * A309778 A309779 A309780 KEYWORD nonn,fini,full AUTHOR Donal LYONS, Aug 17 2019 STATUS approved

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)