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 A262143 #16 May 07 2018 22:04:23
%S A262143 1,1,1,1,3,3,1,8,33,23,1,16,208,1011,371,1,30,768,14336,65985,10515,1,
%T A262143 46,2211,94208,2091520,7536099,461869,1,64,5043,412860,24313856,
%U A262143 535261184,1329205857,28969177,1,96,9984,1361948,164276421,11025776640,211966861312,334169853267,2454072147
%N A262143 Square array read by antidiagonals upwards: the n-th row o.g.f. is exp( Sum_{i >= 1} c(n,i)*x^i/i ) for n >= 1, where c(n,k) is Shanks' array of generalized Euler and class numbers.
%C A262143 Shanks' array c(n,k) n >= 1, k >= 0, is A235605.
%C A262143 We conjecture that the entries of the present array are all integers. More generally, we conjecture that for r = 0,1,2,... and for each n >= 1, the expansion of exp( Sum_{i >= 1} c(n,i + r)*x^i/i ) has integer coefficients. The case n = 1 was conjectured by Hanna in A255895.
%C A262143 For the similarly defined array associated with Shanks' d(n,k) array see A262144.
%H A262143 P. Bala, <a href="/A100100/a100100.pdf">Notes on logarithmic differentiation, the binomial transform and series reversion</a>
%H A262143 William Y. C. Chen, Neil J. Y. Fan, Jeffrey Y. T. Jia, <a href="http://dx.doi.org/10.1090/S0025-5718-2011-02520-2">The generating function for the Dirichlet series Lm(s)</a> Mathematics of Computation, Vol. 81, No. 278, April 2012.
%H A262143 D. Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-1967-0223295-5">Generalized Euler and class numbers</a>. Math. Comp. 21 (1967) 689-694.
%H A262143 D. Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-1968-0227093-9">Corrigenda to: "Generalized Euler and class numbers"</a>, Math. Comp. 22 (1968), 699.
%H A262143 D. Shanks, <a href="/A000003/a000003.pdf">Generalized Euler and class numbers</a>, Math. Comp. 21 (1967), 689-694; 22 (1968), 699. [Annotated scanned copy]
%e A262143 The square array begins (row indexing n starts at 1)
%e A262143 1 1 3 23 371 10515 461869 ..
%e A262143 1 3 33 1011 65985 7536099 1329205857 ..
%e A262143 1 8 208 14336 2091520 535261184 211966861312 ..
%e A262143 1 16 768 94208 24313856 11025776640 7748875976704 ..
%e A262143 1 30 2211 412860 164276421 115699670490 126686112278631 ..
%e A262143 1 46 5043 1361948 778121381 787337024970 1239870854518999 ..
%e A262143 1 64 9984 3716096 2891509760 3978693525504 8522989918683136 ..
%e A262143 ...
%e A262143 Array as a triangle
%e A262143 1
%e A262143 1 1
%e A262143 1 3 3
%e A262143 1 8 33 23
%e A262143 1 16 208 1011 371
%e A262143 1 30 768 14336 65985 10515
%e A262143 1 46 2211 94208 2091520 7536099 461869
%e A262143 1 64 5043 412860 24313856 535261184 1329205857 28969177
%e A262143 1 96 9984 1361948 164276421 11025776640 211966861312 ...
%e A262143 ...
%Y A262143 Cf. A000233 (column 1), A000364 (c(1,n)), A000281 (c(2,n)), A000436 (c(3,n)), A000490 (c(4,n)), A000187 (c(5,n)), A000192 (c(6,n)), A064068 (c(7,n)), A235605, A235606, A255881, A255895, A262144, A262145.
%K A262143 nonn,tabl
%O A262143 1,5
%A A262143 _Peter Bala_, Sep 13 2015