%I M2565 #17 Sep 06 2017 02:47:22
%S 1,3,6,13,24,47,86,159,285,509,895,1565,2708,4660,7964,13543,22912,
%T 38604,64785,108356,180661,300384,498183,824365,1361302,2243799,
%U 3692159,6066161,9952786,16309055,26694132,43646685,71297770,116366274,189774755,309271954,503687536
%N Number of protruded partitions of n with largest part at most 4.
%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 Vincenzo Librandi, <a href="/A005405/b005405.txt">Table of n, a(n) for n = 1..1000</a>
%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)^4/Product(1-x-x^i+x^(1+2*i), i=1..4)-1. - _Emeric Deutsch_, Dec 19 2004
%p G:=(1-x)^4/Product(1-x-x^i+x^(1+2*i),i=1..4)-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)^4/Product[1 - x - x^i + x^(1 + 2 i), {i, 4}] - 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