A058397 Row sums of partition triangle A026820.

1, 3, 6, 13, 22, 42, 66, 112, 172, 270, 397, 602, 858, 1245, 1748, 2464, 3381, 4671, 6302, 8537, 11372, 15147, 19914, 26201, 34057, 44250, 56986, 73277, 93497, 119161, 150809, 190590, 239496, 300388, 374912, 467135, 579394, 717384, 884813

Offset: 1

Author

Wolfdieter Lang, Dec 11 2000

Keywords

• nonn

Crossrefs

Cf. A026820, A046682.

Programs

Maple

seq(add(combinat:-numbpart(n,k),k=0..n),n=1..39); # Peter Luschny, Aug 03 2015

Mathematica

T[n_, k_] := T[n, k] = If[n==0 || k==1, 1, T[n, k-1] + If[k>n, 0, T[n-k, k] ]];
a[n_] := Sum[T[n, k], {k, 1, n}];
Array[a,39] (* Jean-François Alcover, Jun 03 2019, after Alois P. Heinz in A026820 *)

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))

Formula

a(n) = Sum_{k=1..n} A026820(n, k).

a(n) = A278427(2n,n). - John P. McSorley, Nov 28 2016

Extensions

More terms from Benoit Cloitre, Apr 21 2003