A248603 G.f. satisfies: A(x) = Sum_{n>=0} x^n * (A(x) + x^n)^n.

1, 1, 3, 6, 19, 56, 186, 615, 2127, 7467, 26720, 96801, 354901, 1313293, 4900266, 18413166, 69620351, 264673536, 1011100541, 3879382837, 14942671683, 57760251344, 223988614094, 871159201568, 3397330833310, 13281696243924, 52042973504510, 204357290336561, 804029764090404

Offset

0,3

Links

Table of n, a(n) for n=0..28.

Formula

G.f. satisfies: A(x) = Sum_{n>=1} x^(n*(n-1)) / (1 - A(x)*x^n)^n.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 6*x^3 + 19*x^4 + 56*x^5 + 186*x^6 +...
where the g.f. satisfies following series identity:
A(x) = 1 + x*(A(x)+x) + x^2*(A(x)+x^2)^2 + x^3*(A(x)+x^3)^3 + x^4*(A(x)+x^4)^4 + x^5*(A(x)+x^5)^5 + x^6*(A(x)+x^6)^6 +...
A(x) = 1/(1-A(x)*x) + x^2/(1-A(x)*x^2)^2 + x^6/(1-A(x)*x^3)^3 + x^12/(1-A(x)*x^4)^4 + x^20/(1-A(x)*x^5)^5 + x^30/(1-A(x)*x^6)^6 + x^42/(1-A(x)*x^7)^7 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=0, n, x^k * (A + x^k +x*O(x^n))^k)); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=1, sqrtint(2*n+1), x^(k*(k-1)) / (1 - A*x^k +x*O(x^n))^k )); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A345400 A148572 A320174 * A332344 A345244 A052393

Adjacent sequences: A248600 A248601 A248602 * A248604 A248605 A248606

Keyword

nonn

Author

Paul D. Hanna, Oct 09 2014

Status

approved