A068945
Number of ones in the binary expansion of A068943(n).
Original entry on oeis.org
1, 1, 1, 2, 3, 13, 63, 199, 805, 3155, 12319, 48070, 186944, 727997, 2846645, 11109160, 43432775, 169958492, 665601661, 2608395091
Offset: 0
Francois Jooste (phukraut(AT)hotmail.com), Mar 09 2002
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from gmpy2 import popcount
from math import comb, prod
def a(n):
return popcount(prod((n-m+1)**comb(m+n-2, m-1) for m in range(1, n+1)))
print([a(n) for n in range(16)]) # Michael S. Branicky, Apr 09 2023
A068944
Highest power of 9 dividing A068943(n) for n>0.
Original entry on oeis.org
0, 0, 0, 2, 7, 28, 108, 414, 1585, 6087, 23446, 90532, 350343, 1358437, 5276545, 20527950, 79976007, 311984922, 1218474389, 4763911699, 18643889114, 73029856058, 286302435505, 1123267533520, 4410123312095, 17326303720537
Offset: 1
Francois Jooste (phukraut(AT)hotmail.com), Mar 09 2002
a(11)=23446 since f(11,11,11)=9^binomial(12,10) * 6^binomial(15,10) * 3^(18,10) * other terms. this implies a(11)=binomial(12,10) + 1/2*(binomial(15,10)-1 + binomial(18,10)).
Original entry on oeis.org
1, 1, 2, 6, 22, 83, 316, 1213, 4667, 17992, 69509, 269058, 1043346, 4052518, 15764358, 61408219, 239510633, 935245088, 3655841616, 14304538696, 56021145629, 219579741115, 861327333405, 3381084681442, 13281106066320
Offset: 1
Francois Jooste (phukraut(AT)hotmail.com), Mar 10 2002
a(5)=22 since A068943(5)=2524286414780230533120.
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for(n=1,20,print1(ceil((sum(m=1,n,binomial(m+n-2,m-1)*log(n-m+1)))/log(10)),","))
Showing 1-3 of 3 results.
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