A182705 Row sums of triangle A182701.

1, 4, 12, 28, 60, 114, 210, 360, 603, 970, 1529, 2340, 3536, 5222, 7620, 10944, 15555, 21816, 30343, 41740, 56994, 77132, 103684, 138312, 183450, 241696, 316764, 412776, 535340, 690750, 887499, 1135072, 1446060, 1834742, 2319555, 2921616, 3667921, 4589260

Offset: 1

Author

Omar E. Pol, Nov 28 2010

Keywords

• nonn

Links

• Robert Price, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A182700, A182701, A182702, A182704.

Programs

Mathematica

Total /@ Table[n*PartitionsP[n-k], {n, 38}, {k, n}] // Flatten (* Robert Price, Jun 23 2020 *)

PARI

a000070(n) = sum(k=0, n, numbpart(k));
for(n=1, 100, print1(n*a000070(n - 1), ", ")) \\ Indranil Ghosh, Jun 08 2017

Python

from sympy import npartitions as p
def a000070(n): return sum([p(k) for k in range(n + 1)])
def a(n): return n*a000070(n - 1) # Indranil Ghosh, Jun 08 2017

Formula

a(n) = n * A000070(n-1).

G.f.: x*f'(x), where f(x) = (x/(1 - x))*Product_{k>=1} 1/(1 - x^k). - Ilya Gutkovskiy, Jun 08 2017