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 A326998 #19 Feb 19 2025 10:26:47 %S A326998 4,5,31,365,6271,129130,2877421,66628441,1578320767,37983592076, %T A326998 925196176906,22754692780561,564123212097901,14079691134569845, %U A326998 353428830512017081,8915830309096530865,225890912989184760703,5744976464242932324976,146603288011226858621356 %N A326998 a(n) = 1 + binomial(3*n-1, n) + binomial(3*n-1, n-1)*(binomial(2*n-1, n) + 1). %F A326998 From _Mike Sheppard_, Feb 17 2025: (Start) %F A326998 G.f.: (1/6) * (11 + 6/(1 - x) + (12*cos(1/6 arccos(1 - (27*x)/2)))/sqrt(4 - 27*x) + hypergeom([1/3, 2/3], [1], 27*x)). %F A326998 E.g.f.: exp(x) + hypergeom([1/3, 2/3], [1/2, 1], (27*x)/4) + (1/6) * (11 + hypergeom([1/3, 2/3], [1, 1], 27*x)). (End) %p A326998 a := n -> 1 + binomial(3*n-1, n) + binomial(3*n-1, n-1)*(binomial(2*n-1, n) + 1): %p A326998 seq(a(n), n=0..19); %Y A326998 Cf. A327001 (column 3). Essentially the same as A309725. %K A326998 nonn %O A326998 0,1 %A A326998 _Peter Luschny_, Aug 13 2019