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A066187 Sum of the second moments of all partitions of n. 1
0, 1, 7, 23, 66, 145, 321, 600, 1137, 1964, 3379, 5463, 8888, 13714, 21206, 31737, 47319, 68727, 99718, 141488, 200383, 279097, 387302, 530286, 724113, 976949, 1314106, 1751079, 2325412, 3062942, 4022617, 5244455, 6817630, 8808369, 11346219, 14536656, 18573495 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
The first element of each partition is given weight 1.
LINKS
EXAMPLE
a(3) = 23 because the second moments of all partitions of 3 are {3}.{1},{2,1}.{1,4} and {1,1,1}.{1,4,9}, resulting in 3,6,14; summing to 23.
MAPLE
b:= proc(n, i, t) option remember; `if`(n=0, [1, 0],
`if`(i<1, [0$2], `if`(i>n, b(n, i-1, t), b(n, i-1, t)+
(h-> h+[0, h[1]*i*t^2])(b(n-i, i, t+1)))))
end:
a:= n-> b(n$2, 1)[2]:
seq(a(n), n=0..50); # Alois P. Heinz, Jan 29 2014
MATHEMATICA
Table[ Plus@@Map[ #.Range[ Length[ # ]]^2&, IntegerPartitions[ n ]], {n, 30} ]
(* Second program: *)
b[n_, i_, t_] := b[n, i, t] = If[n == 0, {1, 0},
If[i < 1, {0, 0}, If[i > n, b[n, i - 1, t], b[n, i - 1, t] +
# + {0, #[[1]]*i*t^2}& @ b[n - i, i, t + 1]]]];
a[n_] := b[n, n, 1][[2]];
a /@ Range[0, 50] (* Jean-François Alcover, Jun 05 2021, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A343519 A365439 A266801 * A259214 A114246 A297315
KEYWORD
easy,nonn
AUTHOR
Wouter Meeussen, Dec 15 2001
STATUS
approved

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Last modified July 25 03:25 EDT 2024. Contains 374586 sequences. (Running on oeis4.)