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 A010827 #36 Feb 05 2018 16:35:45 %S A010827 1,-21,189,-910,2205,-378,-13321,33345,-10395,-86870,122703,46683, %T A010827 -98287,-264915,96390,1163064,-1113588,-1066527,1042055,536025, %U A010827 2287467,-3603805,-1391733,478170,-562555,13742379,-7889805 %N A010827 Expansion of Product_{k>=1} (1 - x^k)^21. %C A010827 If not n == 0 (mod 7) then a(n) == 0 (mod 7). The reverse is not true, e.g., a(14) = 96390 == (0 mod 7). See the Hardy reference, p. 165. - _Wolfdieter Lang_, Jan 28 2017 %D A010827 G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, AMS Chelsea Publishing, Providence, Rhode Island, 2002, p. 165. %D A010827 Newman, Morris; A table of the coefficients of the powers of eta(tau). Nederl. Akad. Wetensch. Proc. Ser. A. 59 = Indag. Math. 18 (1956), 204-216. %H A010827 Seiichi Manyama, <a href="/A010827/b010827.txt">Table of n, a(n) for n = 0..10000</a> %H A010827 M. Boylan, <a href="http://dx.doi.org/10.1016/S0022-314X(02)00037-9">Exceptional congruences for the coefficients of certain eta-product newforms</a>, J. Number Theory 98 (2003), no. 2, 377-389. MR1955423 (2003k:11071). %H A010827 <a href="/index/Pro#1mxtok">Index entries for expansions of Product_{k >= 1} (1-x^k)^m</a> %F A010827 G.f.: Product_{k>0} (1 - x^k)^21. %F A010827 a(0) = 1, a(n) = -(21/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 27 2017 %F A010827 G.f.: exp(-21*Sum_{k>=1} x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Feb 05 2018 %e A010827 G.f. = 1 - 21*x + 189*x^2 - 910*x^3 + 2205*x^4 - 378*x^5 - 13321*x^6 + 33345*x^7 + ... %t A010827 CoefficientList[Expand@ Product[(1 - x^k)^21, {k, 27}], x, 27] (* _Michael De Vlieger_, Jun 08 2016 *) %t A010827 a[ n_] := SeriesCoefficient[ QPochhammer[ x]^21, {x, 0, n}]; (* _Michael Somos_, Jan 28 2017 *) %o A010827 (PARI) {a(n) = if( n<0, 0, polcoeff( eta(x + x * O(x^n))^21, n))}; /* _Michael Somos_, Jan 28 2017 */ %Y A010827 Cf. A126581. %K A010827 sign %O A010827 0,2 %A A010827 _N. J. A. Sloane_