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

1,2

Links

Table of n, a(n) for n=1..39.

Formula

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

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

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 *)

Prog

(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))

Crossrefs

Cf. A026820, A046682.

Sequence in context: A211870 A239987 A048134 * A174369 A308747 A022811

Adjacent sequences: A058394 A058395 A058396 * A058398 A058399 A058400

Keyword

nonn

Author

Wolfdieter Lang, Dec 11 2000

Extensions

More terms from Benoit Cloitre, Apr 21 2003

Status

approved