cp's OEIS Frontend

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.

A322267 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. (sec(x) + tan(x))^k.

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%I A322267 #5 Dec 09 2018 11:41:41
%S A322267 1,1,0,1,1,0,1,2,1,0,1,3,4,2,0,1,4,9,10,5,0,1,5,16,30,32,16,0,1,6,25,
%T A322267 68,117,122,61,0,1,7,36,130,320,528,544,272,0,1,8,49,222,725,1684,
%U A322267 2709,2770,1385,0,1,9,64,350,1440,4400,9856,15600,15872,7936,0,1,10,81,520,2597,9966,29125,63668,99657,101042,50521,0
%N A322267 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. (sec(x) + tan(x))^k.
%H A322267 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A322267 E.g.f. of column k: (sec(x) + tan(x))^k.
%e A322267 E.g.f. of column k: A_k(x) = 1 + k*x/1! + k^2*x^2/2! + k*(k^2 + 1)*x^3/3! + k^2*(k^2 + 4)*x^4/4! + ...
%e A322267 Square array begins:
%e A322267   1,   1,    1,    1,     1,     1,  ...
%e A322267   0,   1,    2,    3,     4,     5,  ...
%e A322267   0,   1,    4,    9,    16,    25,  ...
%e A322267   0,   2,   10,   30,    68,   130,  ...
%e A322267   0,   5,   32,  117,   320,   725,  ...
%e A322267   0,  16,  122,  528,  1684,  4400,  ...
%t A322267 Table[Function[k, n! SeriesCoefficient[(Sec[x] + Tan[x])^k, {x, 0, n}]][j - n], {j, 0, 11}, {n, 0, j}] // Flatten
%Y A322267 Columns k=0..3 give A000007, A000111, A001250, A292758.
%Y A322267 Main diagonal gives A298244.
%Y A322267 Cf. A322268.
%K A322267 nonn,tabl
%O A322267 0,8
%A A322267 _Ilya Gutkovskiy_, Dec 01 2018