A359718 Column 3 of triangle A359670; a(n) = A359670(n+3,3) for n >= 0.

1, 20, 170, 970, 4410, 17172, 59545, 188700, 556085, 1542640, 4065868, 10253720, 24880705, 58351000, 132750390, 293867786, 634623035, 1339924290, 2771178885, 5623152080, 11211087225, 21989506510, 42478375740, 80897833810, 152022961870, 282119268256, 517394696690

Offset

0,2

Comments

The g.f. G(x,y) of triangle A359670 satisfies: G(x,y) = 1/[Sum_{n=-oo..+oo} (-1)^n * (x*y*G(x,y) + x^n)^n].

Links

Table of n, a(n) for n=0..26.

Prog

(PARI) {a(n) = my(A=1); for(i=1, n+3,
A = 1/sum(m=-#A, #A, (-1)^m * (x*y*A + x^m + x*O(x^(n+3)) )^m ) );
polcoeff( polcoeff( A, n+3, x), 3, y)}
for(n=0, 30, print1( a(n), ", "))
(PARI) {a(n) = my(A=[1]); for(i=1, n+3, A = concat(A, 0);
A[#A] = polcoeff(-y + sum(m=-#A, #A, (-1)^m * x^m * (y*Ser(A) + x^(m-1))^(m+1) )/(-y), #A-1, x) ); polcoeff( A[n+4], 3, y)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A359670.

Sequence in context: A304508 A010826 A022712 * A056128 A027791 A047819

Adjacent sequences: A359715 A359716 A359717 * A359719 A359720 A359721

Keyword

nonn

Author

Paul D. Hanna, Jan 17 2023

Status

approved