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%I #20 Jun 25 2023 16:25:35
%S 1,1,3,6,13,19,37,58,97,143,227,328,492,688,992,1364,1903,2551,3473,
%T 4586,6097,7911,10333,13226,16988,21454,27172,33938,42437,52423,64833,
%U 79354,97130,117824,142930,172018,206925,247179,295105,350154,415124
%N Generating function: 1/((1-x)*(1-x^2)^2*(1-x^3)^3*(1-x^4)^4).
%C Number of partitions of n into parts 1 (of one kind), 2 (of two kinds), 3 (of three kinds), and 4 (of 4 kinds). [_Joerg Arndt_, Jul 11 2013]
%H Ray Chandler, <a href="/A064349/b064349.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (1, 2, 1, 0, -9, -5, 2, 13, 21, -4, -17, -30, -13, 25, 28, 25, -13, -30, -17, -4, 21, 13, 2, -5, -9, 0, 1, 2, 1, -1).
%o (PARI) a(n) = floor( ([13, 28, -44][n%3+1]+(9/2)*(n\3+2)*((n+1)%3-1)) * (n\3+1)/729 - (n\2+1)*(-1)^(n\2) * (3*[-8, 11]+(n\2+2)*(2*[-1, 3]+(n\2+3)*(1/3)*[0, 1]))[n%2+1]/512 + (2*n^9 +270*n^8 +15600*n^7 +504000*n^6 +9977730*n^5 +124629750*n^4 +973069200*n^3 +4521339000*n^2 +11137512613*n +16461579435 +5103*(n+15)*(2*n^4 +120*n^3 +2440*n^2 +19200*n +48213)*(-1)^n) / 20065812480 ) \\ _Tani Akinari_, Jul 12 2013
%o (PARI) Vec(1/((1-x)*(1-x^2)^2*(1-x^3)^3*(1-x^4)^4)+O(x^66)) \\ _Joerg Arndt_, Jul 11 2013
%Y The sequence of sequences A000007, A000012, A008805, A002597, A064349, etc. approaches A000219.
%Y Essentially the same as A002598.
%Y Cf. A002598.
%K nonn
%O 0,3
%A _Henry Bottomley_, Sep 17 2001