A179708 Number of permutations of 1..n having exactly 5 maxima.

0, 7936, 353792, 9061376, 175627264, 2868264960, 41731645440, 559148810240, 7048869314560, 84842998005760, 985278548541440, 11124607890751488, 122829335169859584, 1332091026832097280, 14238886515777208320, 150420440721496473600, 1573853022795658690560

Offset

8,2

Comments

Number of permutations of length n with exactly four valleys.

Links

Table of n, a(n) for n=8..24.

Désiré André, Mémoire sur les séquences des permutations circulaires, Bulletin de la S. M. F., tome 23 (1895), pp. 122-184.

R. G. Rieper and M. Zeleke, Valleyless Sequences, arXiv:math/0005180 [math.CO], 2000.

Formula

G.f.: 256*x^9*(31 - 788*x + 8096*x^2 - 43132*x^3 + 126072*x^4 - 192672*x^5 + 120960*x^6)/ ((1-2*x)^5*(1-4*x)^4*(1-6*x)^3*(1-8*x)^2*(1-10*x)). - Ray Chandler, Dec 06 2011

Crossrefs

Cf. A000079, A000431, A000487, A000517, A130661.

Column k=4 of A008303.

Sequence in context: A185466 A028537 A302901 * A162010 A023322 A064246

Adjacent sequences: A179705 A179706 A179707 * A179709 A179710 A179711

Keyword

nonn

Author

R. H. Hardin, Jul 25 2010

Extensions

More terms from Ray Chandler, Dec 06 2011

Status

approved