A320671 G.f.: 1 / [ Sum_{n>=0} (-1)^n * (2*n+1)*(9*n+1) * x^(n*(n+1)/2) ]^(1/3).

1, 10, 200, 4635, 115400, 2989000, 79413182, 2147670780, 58847999800, 1628799414030, 45443174184489, 1276097550750560, 36027161027614673, 1021735788590470670, 29088548540723602200, 830905722688352466737, 23803614419994729655422, 683666066800944445647240, 19680193160906254634961364, 567666652900351449376374940

Offset

0,2

Comments

Limit a(n+1)/a(n) = 29.8937006274429170027521943552718162106155192278570861849...

Links

Paul D. Hanna, Table of n, a(n) for n = 0..300

Example

G.f.: A(x) = 1 + 10*x + 200*x^2 + 4635*x^3 + 115400*x^4 + 2989000*x^5 + 79413182*x^6 + 2147670780*x^7 + 58847999800*x^8 + 1628799414030*x^9 + ...
such that
1/A(x)^3 = 1 - 30*x + 95*x^3 - 196*x^6 + 333*x^10 - 506*x^15 + 715*x^21 - 960*x^28 + 1241*x^36 - 1558*x^45 + 1911*x^55 - 2300*x^66 + ... + (-1)^n * (2*n+1)*(9*n+1) * x^(n*(n+1)/2) + ...
Note that the nonzero coefficients of 1/A(x)^3 can be generated by
(1 - 27*x + 8*x^2)/(1 + x)^3 = 1 - 30*x + 95*x^2 - 196*x^3 + 333*x^4 + ...
RELATED SERIES.
The cube of the g.f. A(x) equals the g.f. of A320670:
A(x)^3 = 1 + 30*x + 900*x^2 + 26905*x^3 + 804300*x^4 + 24043500*x^5 + 718749221*x^6 + 21486074010*x^7 + 642298264200*x^8 + 19200672023385*x^9 + ... + A320670(n)*x^n + ...

Prog

(PARI) {a(n) = my(A = 1/sum(m=0, sqrtint(2*n+1), (-1)^m * (2*m+1)*(9*m+1) * x^(m*(m+1)/2) +x*O(x^n))^(1/3)); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A320670.

Sequence in context: A126431 A335649 A202436 * A237025 A156275 A036362

Adjacent sequences: A320668 A320669 A320670 * A320672 A320673 A320674

Keyword

nonn

Author

Paul D. Hanna, Oct 18 2018

Status

approved