Original entry on oeis.org
1, 1, 3, 4, 5, 6, 7, 56, 36, 45, 55, 66, 78, 91, 1365, 560, 680, 816, 969, 1140, 1330, 1540, 1771, 42504, 12650, 14950, 17550, 20475, 23751, 27405, 31465, 35960, 40920, 46376, 1623160, 376992, 435897
Offset: 1
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{ v=[0, 1, 2, 5, 9, 14, 20, 27, 83, 119, 164, 219, 285, 363, 454, 1819, 2379, 3059, 3875, 4844, 5984, 7314, 8854, 10625, 53129, 65779, 80729, 98279, 118754, 142505, 169910, 201375, 237335, 278255, 324631, 1947791, 2324783, 2760680]; for (i=1, length(v)-1, print1(v[i+1]-v[i]", ")) }
A102366
Number of subsets of {1,2,...,n} in which exactly half of the elements are less than or equal to sqrt(n).
Original entry on oeis.org
1, 1, 2, 3, 6, 10, 15, 21, 28, 84, 120, 165, 220, 286, 364, 455, 1820, 2380, 3060, 3876, 4845, 5985, 7315, 8855, 10626, 53130, 65780, 80730, 98280, 118755, 142506, 169911, 201376, 237336, 278256, 324632, 1947792, 2324784, 2760681, 3262623, 3838380, 4496388
Offset: 0
a(5) = 10 since the ten subsets of {1,2,3,4,5} are { }, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {1,2, 3,4}, {1,2, 3,5} and {1,2, 4,5}.
Cf.
A011782 for number of subsets with an even number of elements.
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{a(n)=if(n<0,0,binomial(n, sqrtint(n)))} /* Paul D. Hanna */
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{a(n)=sum(k=0,sqrtint(n),binomial(sqrtint(n), k)*binomial(n-sqrtint(n),k))}
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