OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
Cecilia Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube. [Dead link]
Cecilia Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube. [Cached copy, May 15 2013]
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = n*(1 + n)*(2 + n)*(3 + n)*(-1 + n*(2 + n))*(2 + n*(4 + n))/336.
G.f.: x*(1 + 26*x + 66*x^2 + 26*x^3 + x^4)/(1-x)^9. - Colin Barker, Apr 16 2012
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9). - Harvey P. Dale, Feb 20 2015
E.g.f.: x*(336 + 5544*x + 13608*x^2 + 10934*x^3 + 3696*x^4 + 574*x^5 + 40*x^6 + x^7)*exp(x)/336. - G. C. Greubel, Dec 01 2018
Sum_{n>=1} 1/a(n) = 224/3 - 60*sqrt(2)*Pi*cot(sqrt(2)*Pi). - Amiram Eldar, Jan 27 2022
MATHEMATICA
Nest[Accumulate[#]&, Range[30]^5, 3] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 35, 345, 1955, 7990, 26226, 73470, 182490, 412335}, 30] (* Harvey P. Dale, Feb 20 2015 *)
PROG
(PARI) vector(30, n, n*(1+n)*(2+n)*(3+n)*(-1+n*(2+n))*(2+n*(4+n))/336) \\ G. C. Greubel, Dec 01 2018
(Magma) [n*(1+n)*(2+n)*(3+n)*(-1+n*(2+n))*(2+n*(4+n))/336: n in [1..30]]; // G. C. Greubel, Dec 01 2018
(Sage) [n*(1+n)*(2+n)*(3+n)*(-1+n*(2+n))*(2+n*(4+n))/336 for n in (1..30)] # G. C. Greubel, Dec 01 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004
EXTENSIONS
Edited by Ralf Stephan, Dec 16 2004
STATUS
approved