OFFSET
0,2
COMMENTS
FORMULA
G.f.: 1/(1 - G(x)) where G(x) is an o.g.f. of A262002.
a(n) == 0 (mod 10) for n>1.
EXAMPLE
O.g.f.: A(x) = 1 + 2*x + 10*x^2 + 60*x^3 + 400*x^4 + 2900*x^5 + 22700*x^6 +...
where
1 - 1/A(x) = 2*x + 6*x^2 + 28*x^3 + 164*x^4 + 1132*x^5 + 8916*x^6 + 78608*x^7 + 765904*x^8 + 8170752*x^9 +...+ A262002(n)*x^n +...
Note that if we define the logarithmic series:
L(x) = 2*x + 6*x^2/2 + 28*x^3/3 + 164*x^4/4 + 1132*x^5/5 + 8916*x^6/6 + 78608*x^7/7 + 765904*x^8/8 +...+ A262002(n)*x^n/n +...
PROG
(PARI) {a(n) = local(A=1, L=log(sum(m=0, n+1, x^m/m!*prod(k=1, m, k^2+1)) +x*O(x^n))); A=1/(1 - x*L'); polcoeff(A +x*O(x^n), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 08 2015
STATUS
approved