A359725 a(n) = A359720(n+2,1), for n >= 0.

2, 5, 21, 51, 170, 454, 1367, 3776, 11062, 31054, 89935, 254654, 733725, 2088612, 6004175, 17150397, 49267851, 141065942, 405274932, 1162440833, 3341173303, 9596468129, 27600014912, 79359955225, 228397685542, 657335642733, 1893081845674, 5452722985712

Offset: 0

Author

Paul D. Hanna, Jan 14 2023

Keywords

• nonn

Comments

The g.f. of A359720, G(x,y) = Sum_{n>=0} Sum_{k=0..floor(2*n/3)} A359720(n,k)*x^n*y^k, satisfies: x = Sum_{n=-oo..+oo} (-1)^n * x^n * (y + x^n)^n * G(x,y)^n.

Crossrefs

Cf. A359720, A355357, A359726.

Programs

PARI

/* a(n) = A359720(n+2,1) */
{a(n) = my(A=[1]); for(i=1, n+3, A=concat(A, 0);
A[#A] = polcoeff(x - sum(m=-#A, #A, (-1)^m * x^m * (y + x^m +x*O(x^#A) )^m * Ser(A)^m ), #A-1) );
polcoeff( polcoeff(Ser(A), n+2,x), 1,y)}
for(n=0, 30, print1(a(n), ", "))