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A058397 Row sums of partition triangle A026820.

%I A058397 #23 Jun 03 2019 06:45:17
%S A058397 1,3,6,13,22,42,66,112,172,270,397,602,858,1245,1748,2464,3381,4671,
%T A058397 6302,8537,11372,15147,19914,26201,34057,44250,56986,73277,93497,
%U A058397 119161,150809,190590,239496,300388,374912,467135,579394,717384,884813
%N A058397 Row sums of partition triangle A026820.
%F A058397 a(n) = Sum_{k=1..n} A026820(n, k).
%F A058397 a(n) = A278427(2n,n). - _John P. McSorley_, Nov 28 2016
%p A058397 seq(add(combinat:-numbpart(n,k),k=0..n),n=1..39); # _Peter Luschny_, Aug 03 2015
%t A058397 T[n_, k_] := T[n, k] = If[n==0 || k==1, 1, T[n, k-1] + If[k>n, 0, T[n-k, k] ]];
%t A058397 a[n_] := Sum[T[n, k], {k, 1, n}];
%t A058397 Array[a,39] (* _Jean-François Alcover_, Jun 03 2019, after _Alois P. Heinz_ in A026820 *)
%o A058397 (PARI) a(n)=if(n<1,0,polcoeff(sum(k=1,n,1/prod(i=1,k,(1-x^i)),x*O(x^n)),n))
%Y A058397 Cf. A026820, A046682.
%K A058397 nonn
%O A058397 1,2
%A A058397 _Wolfdieter Lang_, Dec 11 2000
%E A058397 More terms from _Benoit Cloitre_, Apr 21 2003