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A303188
a(n) = [x^n] Product_{k=1..n} (1 + (n - k + 1)*x^k).
4
1, 1, 1, 7, 9, 23, 148, 221, 526, 1040, 6767, 9664, 23456, 43943, 91363, 499028, 736410, 1650395, 3107540, 6210372, 10819270, 57864166, 80663444, 179915133, 324882691, 640398244, 1087149284, 2039724322, 9121580902, 12913282685, 27250167385, 48645989650, 92634730208, 156124357449
OFFSET
0,4
LINKS
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