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 A039646 #21 Jul 13 2025 11:02:16
%S A039646 1,18,335,7155,176554,4985316,159168428,5681708100,224518859136,
%T A039646 9737714177928,460132506980640,23537198603711520,1296157111841533824,
%U A039646 76467514565810332800,4812260962479036076800,321826321845522830649600
%N A039646 Third column of Jabotinsky-triangle A038455 related to A006963.
%C A039646 Explicit formula for a(n-3) using partitions of n into 3 parts: cf. Knuth's paper for f(n,3) n >= 3, formula with f(k) := A006963(k+1) = (2*k-1)!/k!, k >= 1.
%H A039646 G. C. Greubel, <a href="/A039646/b039646.txt">Table of n, a(n) for n = 0..362</a>
%H A039646 D. E. Knuth, <a href="http://arxiv.org/abs/math/9207221">Convolution polynomials</a>, arXiv:math/9207221 [math.CA], 1992; Mathematica J. 2.1 (1992), no. 4, 67-78.
%F A039646 a(n) = Sum_{j=0..n} binomial(n+2, j)*A006936(j+2)*A039619(n+2-j).
%F A039646 E.g.f.: log((1-sqrt(1-4*x))/x/2)^3/6. - _Vladeta Jovovic_, May 02 2003
%t A039646 Drop[With[{nmax = 20}, CoefficientList[Series[Log[(1 - Sqrt[1 - 4*x])/x/2]^3/6, {x, 0, nmax}], x]*Range[0, nmax]!], 3] (* _G. C. Greubel_, Dec 14 2017 *)
%o A039646 (PARI) my(x='x+O('x^30)); Vec(serlaplace(log((1-sqrt(1-4*x))/x/2)^3/6)) \\ _G. C. Greubel_, Dec 14 2017
%Y A039646 Cf. A038455, A006963, A039619.
%K A039646 nonn
%O A039646 0,2
%A A039646 _Wolfdieter Lang_