A229182 G.f. satisfies: A(x) = Sum_{n>=0} x^n * Product_{k=1..n} (A(x)^k - x^k).

1, 1, 1, 4, 13, 54, 227, 1019, 4762, 23012, 114487, 583893, 3044598, 16197880, 87798933, 484377698, 2718044549, 15507602279, 89947655628, 530420332747, 3180793948207, 19404122501300, 120475202020535, 761689102469013, 4906578443997601, 32221210135485056, 215818333117100371

Offset

0,4

Links

Table of n, a(n) for n=0..26.

Example

G.f.: A(x) = 1 + x + x^2 + 4*x^3 + 13*x^4 + 54*x^5 + 227*x^6 + 1019*x^7 +...
where g.f. A = A(x) satisfies:
A(x) = 1 + x*(A-x) + x^2*(A-x)*(A^2-x^2) + x^3*(A-x)*(A^2-x^2)*(A^3-x^3) + x^4*(A-x)*(A^2-x^2)*(A^3-x^3)*(A^4-x^4) + x^5*(A-x)*(A^2-x^2)*(A^3-x^3)*(A^4-x^4)*(A^5-x^5) +...

Prog

 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, x^m*prod(k=1, m, A^k-x^k +x*O(x^n)))); polcoeff(A, n)}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Sequence in context: A149467 A149468 A149469 * A149470 A149471 A149472

Adjacent sequences: A229179 A229180 A229181 * A229183 A229184 A229185

Keyword

nonn

Author

Paul D. Hanna, Sep 15 2013

Status

approved