A366731 Expansion of g.f. A(x) satisfying 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (1 - x^(n-1))^(n+1).

1, 1, 0, 2, 2, 6, 19, 41, 99, 307, 750, 2062, 5776, 15674, 43700, 123729, 345728, 982580, 2801615, 7994268, 22953104, 66128105, 190846074, 552959720, 1605817449, 4673526011, 13635237816, 39860703465, 116739997283, 342538898105, 1006709394181, 2963267980415, 8735388348630

Offset

0,4

Comments

a(n) = Sum_{k=0..n} A366730(n,k) for n >= 0.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..300

Formula

G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.

(1) 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (1 - x^(n-1))^(n+1).

(2) 0 = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n-1)) / ( A(x)^n * (1 - x^(n+1))^(n-1) ).

Example

G.f.: A(x) = 1 + x + 2*x^3 + 2*x^4 + 6*x^5 + 19*x^6 + 41*x^7 + 99*x^8 + 307*x^9 + 750*x^10 + 2062*x^11 + 5776*x^12 + 15674*x^13 + 43700*x^14 + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0);
A[#A] = polcoeff( sum(n=-#A, #A, x^n * Ser(A)^n * (1 - x^(n-1))^(n+1) ), #A-2)); A[n+1]}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Cf. A366730, A366732, A366733, A366734, A366735.

Sequence in context: A173098 A370836 A233113 * A341380 A171694 A103179

Adjacent sequences: A366728 A366729 A366730 * A366732 A366733 A366734

Keyword

nonn

Author

Paul D. Hanna, Oct 29 2023

Status

approved