A359726 a(n) = A359720(n+3,2), for n >= 0.

1, 9, 49, 179, 711, 2390, 8361, 27082, 89389, 283170, 905307, 2825245, 8854116, 27341969, 84550769, 259046260, 793589833, 2416512240, 7352490113, 22279068811, 67435591018, 203525629398, 613550161717, 1845654390776, 5545861291941, 16637001197044, 49858191850323

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, A359725.

Programs

PARI

/* a(n) = A359720(n+3,2) */
{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+3,x), 2,y)}
for(n=0, 30, print1(a(n), ", "))