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.

A322268 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. exp(x)*(sec(x) + tan(x))^k.

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%I A322268 #4 Dec 09 2018 11:40:05
%S A322268 1,1,1,1,2,1,1,3,4,1,1,4,9,9,1,1,5,16,29,24,1,1,6,25,67,105,77,1,1,7,
%T A322268 36,129,304,433,294,1,1,8,49,221,705,1519,2029,1309,1,1,9,64,349,1416,
%U A322268 4145,8386,10709,6664,1,1,10,81,519,2569,9601,26385,51007,63025,38177,1,1,11,100,737,4320,19777,69406,181969,340024,409713,243034,1
%N A322268 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. exp(x)*(sec(x) + tan(x))^k.
%H A322268 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A322268 E.g.f. of column k: exp(x)*(sec(x) + tan(x))^k.
%e A322268 E.g.f. of column k: A_k(x) = 1 + (k + 1)*x/1! + (k + 1)^2*x^2/2! + (k^3 + 3*k^2 + 4*k + 1)*x^3/3! + (k^4 + 4*k^3 + 10*k^2 + 8*k + 1)*x^4/4! + ...
%e A322268 Square array begins:
%e A322268   1,   1,    1,     1,     1,     1,  ...
%e A322268   1,   2,    3,     4,     5,     6,  ...
%e A322268   1,   4,    9,    16,    25,    36,  ...
%e A322268   1,   9,   29,    67,   129,   221,  ...
%e A322268   1,  24,  105,   304,   705,  1416,  ...
%e A322268   1,  77,  433,  1519,  4145,  9601,  ...
%t A322268 Table[Function[k, n! SeriesCoefficient[Exp[x] (Sec[x] + Tan[x])^k, {x, 0, n}]][j - n], {j, 0, 11}, {n, 0, j}] // Flatten
%Y A322268 Columns k=0..3 give A000012, A000667, A292756, A292759.
%Y A322268 Main diagonal gives A296793.
%Y A322268 Cf. A322267.
%K A322268 nonn,tabl
%O A322268 0,5
%A A322268 _Ilya Gutkovskiy_, Dec 01 2018