OFFSET
0,4
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..500
EXAMPLE
a(0) = 1;
a(1) = [x^1] (1 + x) = 1;
a(2) = [x^2] (1 + 2*x)*(1 + x^2) = 1;
a(3) = [x^3] (1 + 3*x)*(1 + 2*x^2)*(1 + x^3) = 7;
a(4) = [x^4] (1 + 4*x)*(1 + 3*x^2)*(1 + 2*x^3)*(1 + x^4) = 9;
a(5) = [x^5] (1 + 5*x)*(1 + 4*x^2)*(1 + 3*x^3)*(1 + 2*x^4)*(1 + x^5) = 23, etc.
...
The table of coefficients of x^k in expansion of Product_{k=1..n} (1 + (n - k + 1)*x^k) begins:
n = 0: (1), 0, 0, 0, 0, 0, ...
n = 1: 1, (1), 0, 0, 0, 0, ...
n = 2: 1, 2, (1), 2, 0, 0 ...
n = 3: 1, 3, 2, (7), 3, 2, ...
n = 4: 1, 4, 3, 14, (9), 10, ...
n = 5: 1, 5, 4, 23, 17, (23), ...
MATHEMATICA
Table[SeriesCoefficient[Product[(1 + (n - k + 1) x^k), {k, 1, n}], {x, 0, n}], {n, 0, 33}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 19 2018
STATUS
approved