This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A107702 #22 Oct 02 2023 11:09:48
%S A107702 1,1,1,1,2,1,1,3,6,1,1,4,15,22,1,1,5,28,93,90,1,1,6,45,244,645,394,1,
%T A107702 1,7,66,505,2380,4791,1806,1,1,8,91,906,6345,24868,37275,8558,1,1,9,
%U A107702 120,1477,13926,85405,272188,299865,41586,1,1,10,153,2248,26845,229326,1204245,3080596,2474025,206098,1
%N A107702 Triangle related to guillotine partitions of a k-dimensional box by n hyperplanes.
%C A107702 Row sums are A107703. Transpose of square array A103209, read by antidiagonals.
%H A107702 Seiichi Manyama, <a href="/A107702/b107702.txt">Rows n = 0..139, flattened</a>
%H A107702 E. Ackerman, G. Barequet, R. Y. Pinter and D. Romik, <a href="http://dx.doi.org/10.1016/j.ipl.2006.01.011">The number of guillotine partitions in d dimensions</a>, Inf. Proc. Lett 98 (4) (2006) 162-167.
%F A107702 Number triangle T(n, k)=if(k<=n, sum{j=0..k, C(k+j, 2j)(n-k)^j*C(j)}, 0), C(n) given by A000108.
%e A107702 Triangle begins:
%e A107702 1;
%e A107702 1, 1;
%e A107702 1, 2, 1;
%e A107702 1, 3, 6, 1;
%e A107702 1, 4, 15, 22, 1;
%e A107702 1, 5, 28, 93, 90, 1;
%e A107702 1, 6, 45, 244, 645, 394, 1;
%e A107702 1, 7, 66, 505, 2380, 4791, 1806, 1;
%e A107702 1, 8, 91, 906, 6345, 24868, 37275, 8558, 1;
%e A107702 ...
%o A107702 (PARI) T(n, k) = sum(j=0, k, (n-k)^j*binomial(k+j, 2*j)*binomial(2*j, j)/(j+1)); \\ _Seiichi Manyama_, Oct 02 2023
%Y A107702 Diagonals: A000012, A006318, A103210, A103211, A133305, A133306, A133307, A133308, A133309. - _Philippe Deléham_, Dec 10 2008
%Y A107702 Cf. A000384, A103209.
%K A107702 easy,nonn,tabl
%O A107702 0,5
%A A107702 _Paul Barry_, May 21 2005