Original entry on oeis.org
1, 2, 3, 6, 12, 22, 44, 88, 176, 352, 697, 1394, 2788, 5576, 11152, 22304, 44608, 89172, 178344, 356688, 713376, 1426752, 2853504, 5707008, 11414016, 22828032, 45655636, 91311272, 182622544, 365245088, 730490176, 1460980352, 2921960704, 5843921408
Offset: 0
A242105
Number of sequences (x(k))_{k=1..n}, of n strictly increasing terms of nonnegative integers {x(1)
Original entry on oeis.org
1, 2, 7, 44, 428, 5802, 102322, 2239844, 58849332, 1810039960, 63930543419, 2553881719348, 113979459829296, 5625823639358928, 304505544257483550, 17944306197698666740, 1144180970802458374244, 78517953136289477587608, 5771772521253777092098050
Offset: 0
For n=2 the a(2) = 7 solutions are (0,1), (0,2), (0,3), (0,4), (1,2), (1,3), (1,4).
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a:= proc(n) option remember; `if`(n<2, n+1, add((-1)^(k-1)*
binomial((n-k+1)^2+k-1, k) * a(n-k), k=1..n))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Aug 15 2014
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a[0] = 1; a[1] = 2; a[n_] := a[n] = Sum[(-1)^(k-1)*Binomial[(n-k+1)^2+k-1, k]*a[n-k], {k, 1, n}]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 26 2017 *)
Showing 1-2 of 2 results.
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