

A119907


Number of partitions of n such that if k is the largest part, then k2 occurs as a part.


3



0, 0, 0, 0, 1, 1, 3, 4, 7, 9, 15, 18, 27, 34, 47, 58, 79, 96, 127, 155, 199, 242, 308, 371, 465, 561, 694, 833, 1024, 1223, 1491, 1778, 2150, 2556, 3076, 3642, 4359, 5151, 6133, 7225, 8570, 10066, 11892, 13937, 16401, 19173, 22495, 26228, 30676, 35692, 41620
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,7


COMMENTS

It appears that positive terms give column 3 of triangle A210945.  Omar E. Pol, May 18 2012


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000


FORMULA

G.f. for number of partitions of n such that if k is the largest part, then km occurs as a part is Sum(x^(2*im)/Product(1x^j, j=1..i), i=m+1..infinity).
It appears that a(n) = (A000041(n+2)  A000041(n+1))  (A002620(n+2)  A002620(n+1)).  Gionata Neri, Apr 12 2015


MAPLE

b:= proc(n, i) option remember;
`if`(n=0 or i=1, 1, b(n, i1)+`if`(i>n, 0, b(ni, i)))
end:
a:= n> add(b(n(2*k2), k), k=3..1+n/2):
seq(a(n), n=0..60); # Alois P. Heinz, May 18 2012


MATHEMATICA

b[n_, i_] := b[n, i] = If[n==0  i==1, 1, b[n, i1] + If[i>n, 0, b[ni, i]]]; a[n_] := Sum[b[n(2*k2), k], {k, 3, 1+n/2}]; Table[a[n], {n, 0, 60}] (* JeanFrançois Alcover, Jul 01 2015, after Alois P. Heinz *)


CROSSREFS

Cf. A083751.
Sequence in context: A147953 A163468 A069183 * A241335 A158911 A086772
Adjacent sequences: A119904 A119905 A119906 * A119908 A119909 A119910


KEYWORD

easy,nonn


AUTHOR

Vladeta Jovovic, Aug 02 2006


EXTENSIONS

More terms from Joshua Zucker, Aug 14 2006


STATUS

approved



