A366732 Expansion of g.f. A(x) satisfying 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (2 - x^(n-1))^(n+1).

1, 2, 4, 22, 108, 574, 3224, 18592, 109728, 660938, 4041900, 25034000, 156724204, 990127086, 6304425800, 40416596578, 260658078580, 1689976752116, 11008752656960, 72016455973262, 472912945955364, 3116243639293972, 20599091568973324, 136557058462319178, 907668022344460584

Offset

0,2

Comments

a(n) = Sum_{k=0..n} A366730(n,k) * 2^k for n >= 0.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..250

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 * (2 - x^(n-1))^(n+1).

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

Example

G.f.: A(x) = 1 + 2*x + 4*x^2 + 22*x^3 + 108*x^4 + 574*x^5 + 3224*x^6 + 18592*x^7 + 109728*x^8 + 660938*x^9 + 4041900*x^10 + 25034000*x^11 + ...

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 * (2 - x^(n-1))^(n+1) ), #A-2)); A[n+1]}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Cf. A366730, A366731, A366733, A366734, A366735.

Sequence in context: A080042 A364643 A324145 * A165588 A289191 A235938

Adjacent sequences: A366729 A366730 A366731 * A366733 A366734 A366735

Keyword

nonn

Author

Paul D. Hanna, Oct 29 2023

Status

approved