A054776 - OEIS

A054776

a(n) = 3*n*(3*n-1)*(3*n-2).

0, 6, 120, 504, 1320, 2730, 4896, 7980, 12144, 17550, 24360, 32736, 42840, 54834, 68880, 85140, 103776, 124950, 148824, 175560, 205320, 238266, 274560, 314364, 357840, 405150, 456456, 511920, 571704, 635970, 704880, 778596, 857280, 941094

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OFFSET

0,2

REFERENCES

L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 46.

Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 268.

LINKS

Table of n, a(n) for n=0..33.

Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series")

Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

FORMULA

a(n) = A007531(3n-2) = 6*A006566(n).

Sum_{n>=1} 1/a(n) = Pi*sqrt(3)/12 - log(3)/4 = 0.178796768891527... [Jolley eq. 250]. - Benoit Cloitre, Apr 05 2002

G.f.: 6*x*(1+16*x+10*x^2)/(1-x)^4.

E.g.f.: 3*exp(x)*x*(2 + 18x + 9x^2). - Indranil Ghosh, Apr 15 2017

Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/3 - Pi/(6*sqrt(3)). - Amiram Eldar, Mar 08 2022

MAPLE

A054776:=n->3*n*(3*n-1)*(3*n-2): seq(A054776(n), n=0..50); # Wesley Ivan Hurt, Apr 14 2017

PROG

(PARI) a(n)=3*n*(3*n-1)*(3*n-2)

CROSSREFS