|
|
A258472
|
|
Number of partitions of n into two sorts of parts having exactly 2 parts of the second sort.
|
|
2
|
|
|
1, 4, 11, 24, 49, 89, 158, 262, 428, 667, 1033, 1542, 2289, 3313, 4765, 6717, 9427, 13011, 17882, 24260, 32763, 43775, 58268, 76837, 100953, 131629, 171003, 220683, 283877, 363016, 462794, 587005, 742332, 934536, 1173293, 1467022, 1829538, 2273365, 2817858
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,2
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
b:= proc(n, i) option remember; series(`if`(n=0, 1,
`if`(i<1, 0, add(b(n-i*j, i-1)*add(x^t*
binomial(j, t), t=0..min(2, j)), j=0..n/i))), x, 3)
end:
a:= n-> coeff(b(n$2), x, 2):
seq(a(n), n=2..40);
|
|
MATHEMATICA
|
((Log[1 - x]^2 - Log[1 - x] Log[x] + QPolyGamma[1, x] (2 Log[1 - x] - Log[x] + QPolyGamma[1, x]) + QPolyGamma[1, 1, x])/(2 QPochhammer[x] Log[x]^2) + O[x]^45)[[3]] // Simplify (* Vladimir Reshetnikov, Nov 21 2016 *)
Table[SeriesCoefficient[1/QPochhammer[q + x, q], {x, 0, 2}, {q, 0, n}], {n, 0, 40}] // Simplify (* Vladimir Reshetnikov, Nov 22 2016 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|