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 A096962 #29 Jan 09 2023 01:45:54
%S A096962 1,512,19684,262144,1953126,10078208,40353608,134217728,387440173,
%T A096962 1000000512,2357947692,5160042496,10604499374,20661047296,38445332184,
%U A096962 68719476736,118587876498,198369368576,322687697780,512000262144
%N A096962 a(n) = Sum_{0<d|n, n/d odd} d^9.
%H A096962 Seiichi Manyama, <a href="/A096962/b096962.txt">Table of n, a(n) for n = 1..10000</a>
%H A096962 H. H. Chan and C. Krattenthaler, <a href="https://arxiv.org/abs/math/0407061">Recent progress in the study of representations of integers as sums of squares</a>, arXiv:math/0407061 [math.NT], 2004.
%F A096962 G.f.: Sum_{k>0} k^9 * x^k / (1 - x^(2*k)).
%F A096962 From _Amiram Eldar_, Nov 02 2022: (Start)
%F A096962 Multiplicative with a(2^e) = 2^(9*e) and a(p^e) = (p^(9*e+9)-1)/(p^9-1) for p > 2.
%F A096962 Sum_{k=1..n} a(k) ~ c * n^10, where c = 1023*zeta(10)/10240 = 31*Pi^10/29030400 = 0.100001704136... . (End)
%F A096962 Dirichlet g.f.: zeta(s)*zeta(s-9)*(1-1/2^s). - _Amiram Eldar_, Jan 09 2023
%e A096962 G.f. = q + 512*q^2 + 19684*q^3 + 262144*q^4 + 1953126*q^5 + 10078208*q^6 + ...
%t A096962 a[ n_] := If[ n < 1, 0, Sum[ d^9 Boole[ OddQ[ n/d]], {d, Divisors[ n]}]]; (* _Michael Somos_, Jun 04 2013 *)
%t A096962 a[ n_] := SeriesCoefficient[ With[{u1 = QPochhammer[ q]^8, u2 = QPochhammer[ q^2]^4, u4 = QPochhammer[ q^4]^8}, q u2 (u1 + 32 q u4) (u1^2 + 496 q u4 u1 + 7936 q^2 u4^2 ) / u1], {q, 0, n}]; (* _Michael Somos_, Jun 04 2013 *)
%o A096962 (PARI) {a(n) = if( n<1, 0, sumdiv( n, d, (n/d%2) * d^9))}; /* _Michael Somos_, Jun 04 2013 */
%o A096962 (PARI) {a(n) = local(A, A1, A2, A4); if( n<1, 0, n--; A = x * O(x^n); A1 = eta(x + A)^8; A2 = eta(x^2 + A)^4; A4 = eta(x^4 + A)^8; polcoeff( A2 * (A1 + 32*x * A4) * (A1^2 + 496*x * A1*A4 + 7936*x^2 * A4^2) / A1, n))}; /* _Michael Somos_, Jun 04 2013 */
%o A096962 (Sage) ModularForms( Gamma0(2), 10, prec=33).2; # _Michael Somos_, Jun 04 2013
%o A096962 (Magma) A := Basis( ModularForms( Gamma0(2), 10), 21); A[2] + 512*A[3]; /* _Michael Somos_, Aug 25 2014 */
%Y A096962 Cf. A007331, A013668, A096960, A096961, A096963.
%K A096962 nonn,mult
%O A096962 1,2
%A A096962 _Ralf Stephan_, Jul 18 2004