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%I #13 Oct 04 2018 10:47:30
%S 0,1,5,14,38,85,196,401,830,1615,3119,5802,10718,19246,34276,59889,
%T 103656,176801,299025,499732,828638,1360696,2218128,3586194,5759839,
%U 9184715,14557974,22929745,35916469,55942850,86695329,133671740,205144324,313380895,476667370
%N Total number of parts in all plane partitions of n.
%H Alois P. Heinz, <a href="/A319648/b319648.txt">Table of n, a(n) for n = 0..50</a>
%F a(n) = Sum_{k=1..n} k*A091298(n,k). - _M. F. Hasler_, Sep 27 2018
%e The plane partitions of 2 are [2], [1 1] and [1; 1]. There is a total of a(2) = 5 parts. - _M. F. Hasler_, Sep 27 2018
%o (PARI) A319648(n)={vecsum(apply(pp->vecsum(apply(p->#p,pp)),PlanePartitions(n)))} \\ See A091298 for PlanePartitions(). For illustration mainly, becomes slow for n > 15. - _M. F. Hasler_, Sep 27 2018
%o (PARI) M319648=[]; A319648(n,L=0,s)={if(L, n>1||return([1,1]); #L>2||(s=setsearch(M319648,[[n,L],[]],1))>#M319648|| M319648[s][1]!=[n,L]|| return(M319648[s][2]); my(S=[1,n]); for(m=2,n, forpart(P=m, vecmin(L-Vecrev(P,#L))<0&&next; S+=if(m<n,A319648(n-m,Vecrev(P))*[1,#P;0,1],[1,#P]),L[1],#L)); #L>2|| M319648=setunion(M319648,[[[n,L],S]]); S, my(S=n); n>1&& forpart(P=n,S+=#P); for(m=2,n-1,forpart(P=m,S+=A319648(n-m,Vecrev(P))*[#P,1]~));S)} \\ _M. F. Hasler_, Sep 30 2018
%Y Row sums of A092288.
%Y Cf. A000219.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Sep 25 2018
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