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A003403 G.f.: (1 + x^3 + x^4 + ... + x^12 + x^15)/Product_{i=1..10} (1 - x^i).

%I A003403 M1049 #34 Jan 31 2024 10:48:00
%S A003403 1,1,2,4,7,11,18,27,41,60,87,122,172,235,320,430,572,751,982,1268,
%T A003403 1629,2074,2625,3297,4123,5118,6324,7771,9506,11567,14023,16917,20335,
%U A003403 24343,29039,34510,40885,48265,56811,66661,78001,91001,105901,122902,142291,164329,189347
%N A003403 G.f.: (1 + x^3 + x^4 + ... + x^12 + x^15)/Product_{i=1..10} (1 - x^i).
%C A003403 Enumerates certain triangular arrays of integers.
%D A003403 J. C. P. Miller, On the enumeration of partially ordered sets of integers, pp. 109-124 of T. P. McDonough and V. C. Mavron, editors, Combinatorics: Proceedings of the Fourth British Combinatorial Conference 1973. London Mathematical Society, Lecture Note Series, Number 13, Cambridge University Press, NY, 1974. The g.f. is in Eq. (10.5).
%D A003403 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003403 Ray Chandler, <a href="/A003403/b003403.txt">Table of n, a(n) for n = 0..1000</a>
%H A003403 <a href="/index/Rec#order_40">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 1, 0, -2, -2, -3, 0, 2, 5, 4, 4, -2, -5, -6, -7, -2, 1, 7, 8, 7, 1, -2, -7, -6, -5, -2, 4, 4, 5, 2, 0, -3, -2, -2, 0, 1, 1, 1, -1).
%p A003403 (1+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^15)/mul(1-x^i,i=1..10);
%t A003403 CoefficientList[Series[(1+Total[x^Range[3,12] ]+x^15)/Product[1 - x^i, {i,10}], {x,0,50}],x] (* _Harvey P. Dale_, Jun 24 2018 *)
%Y A003403 Cf. A003402, A003404, A003405, A029073, A256975, A256976, A256977.
%K A003403 nonn
%O A003403 0,3
%A A003403 _N. J. A. Sloane_
%E A003403 Entry revised by _N. J. A. Sloane_, Apr 22 2015