OFFSET
0,2
COMMENTS
Row sums of triangle A143228.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) ~ exp(2*sqrt(2*n/3)*Pi)/(8*sqrt(6)*Pi*n^(3/2)) * (1 + (5*Pi/(12*sqrt(6)) - sqrt(3/2)/Pi)/sqrt(n) + (13*Pi^2/1728 - 19/48)/n). - Vaclav Kotesovec, Nov 04 2016
EXAMPLE
MATHEMATICA
A143229[n_]:= PartitionsP[n]*Sum[PartitionsP[k], {k, 0, n}];
Table[A143229[n], {n, 0, 50}] (* G. C. Greubel, Aug 27 2024 *)
PROG
(Magma)
A143229:= func< n | NumberOfPartitions(n)*(&+[NumberOfPartitions(k): k in [0..n]]) >;
[A143229(n): n in [0..50]]; // G. C. Greubel, Aug 27 2024
(SageMath)
def p(n): return number_of_partitions(n) # A000041
def A143229(n): return p(n)*sum(p(k) for k in range(n+1))
[A143229(n) for n in range(51)] # G. C. Greubel, Aug 27 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Jul 31 2008
EXTENSIONS
More terms from Vaclav Kotesovec, Nov 04 2016
STATUS
approved