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 A129123 Number of 4-tuples of standard tableau with height less than or equal to 2. 3
 1, 1, 2, 17, 98, 882, 7812, 78129, 815474, 8955650, 101869508, 1194964498, 14374530436, 176681194276, 2212121332488, 28145258688369, 363177582488274, 4745064935840178, 62687665026816228, 836447728509168930 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS F. Bergeron, L. Favreau and D. Krob, Conjectures on the enumeration of tableaux of bounded height, Discrete Math, vol. 139, no. 1-3 (1995), 463-468. FORMULA a(n) = Sum_{k=0..n} A120730(n,k)^4. [Philippe Deléham, Oct 18 2008] From Vaclav Kotesovec, Dec 16 2017: (Start) Recurrence: n*(n+1)^3*(15*n^2 - 34*n + 7)*a(n) = 2*n*(90*n^5 - 309*n^4 + 147*n^3 + 124*n^2 - 135*n + 35)*a(n-1) + 4*(n-1)^2*(4*n - 5)*(4*n - 3)*(15*n^2 - 4*n - 12)*a(n-2). a(n) ~ 3* 2^(4*n - 1/2) / (Pi^(3/2) * n^(7/2)). (End) MATHEMATICA Table[Sum[(Binomial[n, k] - Binomial[n, k-1])^4, {k, 0, Floor[n/2]}], {n, 0, 20}] (* Vaclav Kotesovec, Dec 16 2017 *) PROG (PARI) a(n)=sum(k=0, n\2, (binomial(n, k)-binomial(n, k-1))^4) CROSSREFS Cf. A001405, A000108, A003161. Sequence in context: A002645 A100268 A163790 * A109724 A127533 A023260 Adjacent sequences:  A129120 A129121 A129122 * A129124 A129125 A129126 KEYWORD nonn AUTHOR Mike Zabrocki, Mar 29 2007 STATUS approved

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Last modified January 17 16:50 EST 2019. Contains 319235 sequences. (Running on oeis4.)