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A202980
G.f.: [ Sum_{n>=0} (n+1)*(n+2)*(n+3)/3! * 3^(n*(n-1)) * x^n ]^(1/4).
1
1, 1, 21, 3581, 4638641, 48800828001, 4323567045653269, 3282556699972913697517, 21588080014422603968890377825, 1239061910207197852963732743864398913, 624049391401084282980615178692488088532058133
OFFSET
0,3
COMMENTS
Compare g.f. to: [Sum_{n>=0} (n+1)*(n+2)*(n+3)/3! * x^n ]^(1/4) = 1/(1-x).
FORMULA
a(n) == 1 (mod 4).
EXAMPLE
G.f.: A(x) = 1 + x + 21*x^2 + 3581*x^3 + 4638641*x^4 + 48800828001*x^5 +...
where
A(x)^4 = 1 + 4*x + 10*3^2*x^2 + 20*3^6*x^3 + 35*3^12*x^4 + 56*3^20*x^5 +...
more explicitly,
A(x)^4 = 1 + 4*x + 90*x^2 + 14580*x^3 + 18600435*x^4 + 195259926456*x^5 +...
PROG
(PARI) {a(n)=polcoeff(sum(m=0, n, (m+1)*(m+2)*(m+3)/3!*3^(m*(m-1))*x^m+x*O(x^n))^(1/4), n)}
CROSSREFS
Cf. A202943.
Sequence in context: A078395 A340331 A370085 * A221722 A153833 A221164
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 26 2011
STATUS
approved