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.

A350738 Expansion of Sum_{k>=0} (-1)^k * x^(k^2) * Product_{j=1..k} (1+x^j).

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%I A350738 #17 Jan 14 2022 16:18:36
%S A350738 1,-1,-1,0,1,1,1,1,0,-1,-1,-1,-2,-1,-1,-1,1,1,1,2,2,2,2,2,1,0,0,-1,-2,
%T A350738 -2,-3,-3,-3,-3,-3,-3,-1,-1,0,1,1,3,4,4,4,5,5,5,5,3,3,3,1,0,-1,-3,-4,
%U A350738 -4,-6,-7,-7,-8,-8,-8,-7,-7,-6,-5,-4,-2,-1,1,3,5,6,8,9,10,12,13,13,12,13,12,11,11,9,7,5,3,0
%N A350738 Expansion of Sum_{k>=0} (-1)^k * x^(k^2) * Product_{j=1..k} (1+x^j).
%H A350738 Seiichi Manyama, <a href="/A350738/b350738.txt">Table of n, a(n) for n = 0..10000</a>
%o A350738 (PARI) my(N=99, x='x+O('x^N)); Vec(sum(k=0, sqrtint(N), (-1)^k*x^k^2*prod(j=1, k, 1+x^j)))
%o A350738 (Python)
%o A350738 from math import prod, isqrt
%o A350738 from sympy import Poly
%o A350738 from sympy.abc import x
%o A350738 def A350738(n): return Poly(sum((-1 if k % 2 else 1)*x**(k**2)*prod(1+x**j for j in range(1,k+1)) for k in range(isqrt(n+1)+1))).all_coeffs()[-n-1] # _Chai Wah Wu_, Jan 14 2022
%Y A350738 Cf. A039924, A306734, A350310, A350737.
%K A350738 sign,look
%O A350738 0,13
%A A350738 _Seiichi Manyama_, Jan 12 2022