A199544 G.f.: A(x) = Sum_{n>=0} x^n * A(x)^(n^2) * (1 - A(x)^(2*n+1))/(1 - A(x)).

1, 3, 23, 271, 3876, 61809, 1057324, 18999550, 354126904, 6790260312, 133193201306, 2661966127599, 54046089492190, 1112240570177203, 23161201079072759, 487383250552812705, 10353102122586909350, 221819714961583800336, 4790442570608936302923

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Example

G.f.: A(x) = 1 + 3*x + 23*x^2 + 271*x^3 + 3876*x^4 + 61809*x^5 +...
where the g.f. A = A(x) satisfies the equivalent expressions:
A = 1 + x*A*(1-A^3)/(1-A) + x^2*A^4*(1-A^5)/(1-A) + x^3*A^9*(1-A^7)/(1-A) + x^4*A^16*(1-A^9)/(1-A) + x^5*A^25*(1-A^11)/(1-A) +...
A = 1 + x*(A + A^2 + A^3) + x^2*(A^4 + A^5 + A^6 + A^7 + A^8) + x^3*(A^9 + A^10 + A^11 + A^12 + A^13 + A^14 + A^15) +...

Prog

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

Crossrefs

Cf. A199543, A199409.

Sequence in context: A159017 A004700 A378114 * A302117 A343772 A006555

Adjacent sequences: A199541 A199542 A199543 * A199545 A199546 A199547

Keyword

nonn

Author

Paul D. Hanna, Nov 07 2011

Status

approved