A202980 - OEIS

A202980

G.f.: [ Sum_{n>=0} (n+1)*(n+2)*(n+3)/3! * 3^(n*(n-1)) * x^n ]^(1/4).

1, 1, 21, 3581, 4638641, 48800828001, 4323567045653269, 3282556699972913697517, 21588080014422603968890377825, 1239061910207197852963732743864398913, 624049391401084282980615178692488088532058133

(list; graph; refs; listen; history; text; internal format)

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).

LINKS

Table of n, a(n) for n=0..10.

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

Adjacent sequences: A202977 A202978 A202979 * A202981 A202982 A202983

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 26 2011

STATUS

approved