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

1,2

Links

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

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A182700, A182701, A182702, A182704.

Sequence in context: A028346 A356728 A079089 * A186924 A261320 A179023

Adjacent sequences: A182702 A182703 A182704 * A182706 A182707 A182708

Keyword

nonn

Author

Omar E. Pol, Nov 28 2010

Status

approved