A326998 a(n) = 1 + binomial(3*n-1, n) + binomial(3*n-1, n-1)*(binomial(2*n-1, n) + 1).

4, 5, 31, 365, 6271, 129130, 2877421, 66628441, 1578320767, 37983592076, 925196176906, 22754692780561, 564123212097901, 14079691134569845, 353428830512017081, 8915830309096530865, 225890912989184760703, 5744976464242932324976, 146603288011226858621356

Offset: 0

Author

Peter Luschny, Aug 13 2019

Keywords

• nonn

Crossrefs

Cf. A327001 (column 3). Essentially the same as A309725.

Programs

Maple

a := n -> 1 + binomial(3*n-1, n) + binomial(3*n-1, n-1)*(binomial(2*n-1, n) + 1):
seq(a(n), n=0..19);

Formula

From Mike Sheppard, Feb 17 2025: (Start)

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)).

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)