Arsenii Abdrafikov has authored 2 sequences.
A245240
Coefficients of the series reversion of the series Sum(x^k for k in A008578).
Original entry on oeis.org
0, 1, -1, 1, 0, -5, 21, -59, 117, -95, -484, 3131, -11219, 28216, -40975, -49778, 630853, -2758309, 8205948, -16014181, 3933569, 135111669, -743995720, 2566032656, -6105683945, 6584104436, 26402611080, -205994058892, 825490609412, -2295266373781
Offset: 0
x - x^2 + x^3 - 5*x^5 + 21*x^6 + ...
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With[{N = 10}, CoefficientList[InverseSeries[x + Sum[x^Prime[k], {k, 1, N}] + O[x]^(Prime[N + 1] - 1)], x]]
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t=Ser(x+O(x^31)); forprime(p=2,30,t+=x^p); Vec(serreverse(t)) /* Max Alekseyev, Jul 15 2014 */
A222659
Table a(m,n) read by antidiagonals, m, n >= 1, where a(m,n) is the number of divide-and-conquer partitions of an m X n rectangle into integer sub-rectangles.
Original entry on oeis.org
1, 2, 2, 4, 8, 4, 8, 34, 34, 8, 16, 148, 320, 148, 16, 32, 650, 3118, 3118, 650, 32, 64, 2864, 30752, 68480, 30752, 2864, 64, 128, 12634, 304618, 1525558, 1525558, 304618, 12634, 128
Offset: 1
Table begins:
1, 2, 4, 8, 16, 32, 64, ...
2, 8, 34, 148, 650, 2864, 12634, ...
4, 34, 320, 3118, 30752, 304618, 3022112, ...
8, 148, 3118, 68480, 1525558, ...
16, 650, 30752, 1525558, ...
32, 2864, 304618, ...
64, 12634, 3022112, ...
Not every partition (cf. A116694) into integer sub-rectangles is divide-and-conquer. For example, the following partition of a 3 X 3 rectangle into 5 sub-rectangles is not divide-and-conquer:
112
342
355
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