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 A383701 #12 May 07 2025 06:03:36
%S A383701 0,0,0,1,28,730,20460,633619,21740040,823020596,34174098440,
%T A383701 1546855384261,75883563554436,4013184755214414,227719025845257492,
%U A383701 13804358188086757719,890571834923460488784,60933371174617735181160,4407783770975985847999440,336154167664942342604334345
%N A383701 Coefficient of x^3 in expansion of (x+1) * (x+5) * ... * (x+4*n-3).
%F A383701 a(n) = Sum_{k=3..n} 4^(n-k) * binomial(k,3) * |Stirling1(n,k)|.
%F A383701 a(n) = Sum_{k=3..n} (4*n-3)^(k-3) * 4^(n-k) * binomial(k,3) * Stirling1(n,k).
%F A383701 E.g.f.: f(x) * log(f(x))^3 / 6, where f(x) = 1/(1 - 4*x)^(1/4).
%F A383701 Conjecture D-finite with recurrence a(n) +4*(-4*n+9)*a(n-1) +2*(48*n^2-264*n+371)*a(n-2) -4*(4*n-13)*(16*n^2-104*n+173)*a(n-3) +(4*n-15)^4*a(n-4)=0. - _R. J. Mathar_, May 07 2025
%o A383701 (PARI) a(n) = polcoef(prod(k=0, n-1, x+4*k+1), 3);
%Y A383701 Column k=3 of A290319.
%K A383701 nonn
%O A383701 0,5
%A A383701 _Seiichi Manyama_, May 06 2025