A248426 Number of permutations of length n avoiding the pattern 1342 and with 1 appearing before n.

1, 3, 11, 46, 211, 1038, 5400, 29425, 166767, 977637, 5901299, 36538483, 231286924, 1492482109, 9793849702, 65217085321, 439887071563, 3000650380603, 20673092451143, 143687057466690, 1006538694994567, 7100409431126274, 50404258628152846, 359845398688215262

Offset: 2

Author

Nathaniel Shar, Oct 06 2014

Keywords

• nonn

Examples

			For n=4 the 11 permutations are: 1234, 1243, 1324, 1423, 1432, 2134, 2143, 2314, 3124, 3142, 3214.
		

Crossrefs

Cf. A022558.

Formula

G.f.: (-1 + sqrt((8*x-1)*sqrt(1-8*x) - 136*x^2 + 20*x + 1)/sqrt((8*x-1)*sqrt(1-8*x) - 8*x^2 + 20*x + 1))*((8*x-1)*sqrt(1-8*x) - 8*x^2 - 12*x + 1)/(64*x).