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%I M2569 #16 Sep 06 2017 03:26:43
%S 1,3,6,13,25,49,91,170,309,558,992,1752,3062,5317,9166,15712,26784,
%T 45447,76775,129203,216662,362177,603671,1003566,1664389,2754382,
%U 4549207,7500096,12344840,20288723,33298979,54584077,89373081,146182754
%N Number of protruded partitions of n with largest part at most 5.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D R. P. Stanley, Ordered structures and partitions, Memoirs of the Amer. Math. Soc., no. 119 (1972).
%H R. P. Stanley, <a href="http://www.fq.math.ca/Scanned/13-3/stanley.pdf">A Fibonacci lattice</a>, Fib. Quart., 13 (1975), 215-232.
%F G.f.: (1-x)^5/Product(1-x-x^i+x^(1+2*i), i=1..5)-1. - _Emeric Deutsch_, Dec 19 2004
%p G:=(1-x)^5/Product(1-x-x^i+x^(1+2*i),i=1..5)-1: Gser:=series(G,x=0,39): seq(coeff(Gser,x^n),n=1..37); # _Emeric Deutsch_, Dec 19 2004
%t Rest@ CoefficientList[Series[(1 - x)^5/Product[1 - x - x^i + x^(1 + 2 i), {i, 5}] - 1, {x, 0, 34}], x] (* _Michael De Vlieger_, Sep 05 2017 *)
%K nonn
%O 1,2
%A _N. J. A. Sloane_.
%E More terms from _Emeric Deutsch_, Dec 19 2004
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