A341960 G.f. A(x) satisfies: A(x) = Product_{n>=0} (1-x^(5*n+1)*A(x)) * (1-x^(5*n+4)*A(x)) / ( (1-x^(5*n+2)*A(x)) * (1-x^(5*n+3)*A(x)) ).

1, -1, 2, -3, 5, -9, 17, -35, 78, -180, 424, -1007, 2397, -5717, 13671, -32808, 79074, -191458, 465654, -1137279, 2788086, -6858079, 16919890, -41856203, 103796588, -257976965, 642512314, -1603329098, 4008201233, -10037187453, 25174707801, -63236031835, 159064703284

Offset

0,3

Comments

Compare to Ramanujan's continued fraction (A007325): R(x) = Product_{n>=0} (1 - x^(5*n+1))*(1 - x^(5*n+4)) / ( (1 - x^(5*n+2))*(1 - x^(5*n+3)) ) = 1/(1 + x/( 1 + x^2/( 1 + x^3/( 1 + x^4/ ... )))).

Links

Table of n, a(n) for n=0..32.

Example

G.f.: A(x) = 1 - x + 2*x^2 - 3*x^3 + 5*x^4 - 9*x^5 + 17*x^6 - 35*x^7 + 78*x^8 - 180*x^9 + 424*x^10 - 1007*x^11 + 2397*x^12 - 5717*x^13 + 13671*x^14 + ...

Prog

(PARI) {a(n) = my(A=1); for(i=1, n,
A = prod(m=0, n, (1-x^(5*m+1)*A)*(1-x^(5*m+4)*A)/((1-x^(5*m+2)*A)*(1-x^(5*m+3)*A +x*O(x^n) )) ) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A007325.

Sequence in context: A166286 A179807 A110113 * A137155 A014227 A334816

Adjacent sequences: A341957 A341958 A341959 * A341961 A341962 A341963

Keyword

sign

Author

Paul D. Hanna, Mar 16 2021

Status

approved