|
| |
|
|
A366732
|
|
Expansion of g.f. A(x) satisfying 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (2 - x^(n-1))^(n+1).
|
|
7
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
a(n) = Sum_{k=0..n} A366730(n,k) * 2^k for n >= 0.
|
|
|
LINKS
|
|
|
|
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
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
