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A199410 G.f. satisfies: A(x) = Sum_{n>=0} A(x)^n * x^(n*(n+1)/2) * (1 - x^(n+1))/(1 - x). 2
1, 1, 2, 4, 9, 21, 50, 122, 303, 763, 1943, 4996, 12953, 33824, 88877, 234824, 623474, 1662618, 4451171, 11959159, 32235236, 87145035, 236226761, 641942519, 1748479813, 4772529625, 13052515077, 35763350619, 98158386548, 269844628977, 742940020480, 2048366903124, 5655092015428 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

Define f(z,q) = Sum_{n>=0} z^n * q^(n*(n+1)/2) then g.f. A(q) satisfies:

A(q) = (f(A(q),q) - q*f(q*A(q),q))/(1-q).

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 21*x^5 + 50*x^6 + 122*x^7 +...

where the g.f. satisfies the equivalent expressions:

A(x) = 1 + A(x)*x*(1-x^2)/(1-x) + A(x)^2*x^3*(1-x^3)/(1-x) + A(x)^3*x^6*(1-x^4)/(1-x) + A(x)^4*x^10*(1-x^5)/(1-x) +...

A(x) = 1 + A(x)*(x + x^2) + A(x)^2*(x^3 + x^4 + x^5) + A(x)^3*(x^6 + x^7 + x^8 + x^9) + A(x)^4*(x^10 + x^11 + x^12 + x^13 + x^14) +...

PROG

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, sqrtint(2*n+1), A^m*x^(m*(m+1)/2)*(1-x^(m+1))/(1-x))+x*O(x^n)); polcoeff(A, n)}

CROSSREFS

Cf. A199409.

Sequence in context: A238438 A257104 A318008 * A091600 A261232 A176334

Adjacent sequences:  A199407 A199408 A199409 * A199411 A199412 A199413

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 06 2011

STATUS

approved

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Last modified December 1 21:42 EST 2020. Contains 338858 sequences. (Running on oeis4.)