A101214 a(n) = n * (n+1)^2 * (n+2)^3 * (n+3)^4.

0, 27648, 720000, 7776000, 51861600, 252887040, 987614208, 3265920000, 9487368000, 24839654400, 59717623680, 133689523968, 281719620000, 563576832000, 1077621350400, 1980468817920, 3514388300928, 6044699520000, 10109900304000, 16487780601600, 26281368257760

Offset

0,2

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

G.f.: -288*x*(x^6+109*x^5+1435*x^4+4735*x^3+4780*x^2+1444*x+96) / (x-1)^11. - Colin Barker, Jul 04 2015

From Amiram Eldar, Apr 03 2021: (Start)

Sum_{n>=1} 1/a(n) = -20129/7776 + 175*Pi^2/648 + Pi^4/1080 - 5*zeta(3)/36.

Sum_{n>=1} (-1)^(n+1)/a(n) = 30311/7776 - 13*Pi^2/1296 - 7*Pi^4/8640 - 344*log(2)/81 - 31*zeta(3)/48. (End)

Example

a(1) = 1 * (1+1)^2 * (1+2)^3 * (1+3)^4 = 27648.

Mathematica

Table[n*(n + 1)^2*(n + 2)^3*(n + 3)^4, {n, 0, 20}] (* Stefan Steinerberger, Feb 26 2006 *)

Prog

(Maxima) A101214(n):=n*(n+1)^2*(n+2)^3*(n+3)^4$ makelist(A101214(n), n, 0, 20); /* Martin Ettl, Dec 15 2012 */
(PARI) a(n) = n * (n+1)^2 * (n+2)^3 * (n+3)^4 \\ Colin Barker, Jul 04 2015
(PARI) concat(0, Vec(-288*x*(x^6 +109*x^5 +1435*x^4 +4735*x^3 +4780*x^2 +1444*x +96)/(x -1)^11 + O(x^100))) \\ Colin Barker, Jul 04 2015

Crossrefs

Cf. A101213.

Sequence in context: A025309 A097244 A350185 * A339257 A202589 A079321

Adjacent sequences: A101211 A101212 A101213 * A101215 A101216 A101217

Keyword

nonn,easy

Author

Parthasarathy Nambi, Dec 13 2004

Extensions

More terms from Stefan Steinerberger, Feb 26 2006

Status

approved