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A193113 G.f. satisfies: 1 = Sum_{n>=0} (-x)^(n*(n+1)/2) * A(x)^(3*n+1). 5
1, 1, 4, 23, 151, 1074, 8059, 62814, 503619, 4126954, 34411602, 291025337, 2490377810, 21523367553, 187603609077, 1647252368595, 14556722879278, 129366008725176, 1155458240271571, 10366549508487178, 93382085749705066, 844255894224907354 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..21.

FORMULA

G.f. A(x) satisfies the continued fraction:

1 = A(x)/(1+ x*A(x)^3/(1- x*(1+x)*A(x)^3/(1+ x^3*A(x)^3/(1+ x^2*(1-x^2)*A(x)^3/(1+ x^5*A(x)^3/(1- x^3*(1+x^3)*A(x)^3/(1+ x^7*A(x)^3/(1+ x^4*(1-x^4)*A(x)^3/(1- ...)))))))))

due to an identity of a partial elliptic theta function.

EXAMPLE

G.f.: A(x) = 1 + x + 4*x^2 + 23*x^3 + 151*x^4 + 1074*x^5 + 8059*x^6 +...

which satisfies:

1 = A(x) - x*A(x)^4 - x^3*A(x)^7 + x^6*A(x)^10 + x^10*A(x)^13 - x^15*A(x)^16 - x^21*A(x)^19 ++--...

Related expansions.

A(x)^4 = 1 + 4*x + 22*x^2 + 144*x^3 + 1025*x^4 + 7696*x^5 +...

A(x)^7 = 1 + 7*x + 49*x^2 + 364*x^3 + 2814*x^4 + 22400*x^5 +...

PROG

(PARI) {a(n)=local(A=[1]); for(i=1, n, A=concat(A, 0); A[#A]=polcoeff(1-sum(m=0, sqrtint(2*(#A))+1, (-x)^(m*(m+1)/2)*Ser(A)^(3*m+1)), #A-1)); if(n<0, 0, A[n+1])}

CROSSREFS

Cf. A193111, A193112, A193114, A193115, A193116.

Sequence in context: A194006 A116881 A107089 * A192730 A246813 A055723

Adjacent sequences:  A193110 A193111 A193112 * A193114 A193115 A193116

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 16 2011

STATUS

approved

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Last modified August 4 11:27 EDT 2021. Contains 346447 sequences. (Running on oeis4.)