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A182705
Row sums of triangle A182701.
3
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
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
KEYWORD
nonn
AUTHOR
Omar E. Pol, Nov 28 2010
STATUS
approved