A062194 Fifth column sequence of triangle A062139 (generalized a=2 Laguerre).

1, 35, 840, 17640, 352800, 6985440, 139708800, 2854051200, 59935075200, 1298593296000, 29088489830400, 674324082432000, 16183777978368000, 402104637462528000, 10339833534750720000, 275039572024369152000

Offset

0,2

Links

Harry J. Smith, Table of n, a(n) for n = 0..100

Index entries for sequences related to Laguerre polynomials.

Formula

E.g.f.: (1 + 24*x + 90*x^2 + 80*x^3 + 15*x^4)/(1-x)^11.

a(n) = A062139(n+4, 4).

a(n) = (n+4)!*binomial(n+6, 6)/4!.

If we define f(n,i,x) = Sum_{k=i..n} Sum_{j=i..n} binomial(k,j) * Stirling1(n,k) * Stirling2(j,i) * x^(k-j) then a(n-4) = (-1)^n*f(n,4,-7), (n >= 4). - Milan Janjic, Mar 01 2009

From Amiram Eldar, May 06 2022: (Start)

Sum_{n>=0} 1/a(n) = 336*(gamma - Ei(1)) - 96*e + 3524/5, where gamma = A001620, Ei(1) = A091725, and e = A001113.

Sum_{n>=0} (-1)^n/a(n) = 3264*(gamma - Ei(-1)) - 1920/e - 9464/5, where Ei(-1) = -A099285. (End)

Mathematica

Table[(n+4)!*Binomial[n+6, 6]/4!, {n, 0, 20}] (* G. C. Greubel, May 12 2018 *)

Prog

(Sage) [binomial(n, 6)*factorial (n-2)/factorial (4) for n in range(6, 22)] # Zerinvary Lajos, Jul 07 2009
(PARI) { f=6; for (n=0, 100, f*=n + 4; write("b062194.txt", n, " ", f*binomial(n + 6, 6)/24) ) } \\ Harry J. Smith, Aug 02 2009
(Magma) [Factorial(n+4)*Binomial(n+6, 6)/Factorial(4): n in [0..20]]; // G. C. Greubel, May 12 2018
(GAP) List([0..15], n->Factorial(n+4)*Binomial(n+6, 6)/Factorial(4)); # Muniru A Asiru, Jul 01 2018

Crossrefs

Cf. A001710, A005461, A005990, A062193.

Cf. A001113, A001620, A091725, A099285.

Sequence in context: A109508 A267834 A001724 * A004372 A080250 A014934

Adjacent sequences: A062191 A062192 A062193 * A062195 A062196 A062197

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 19 2001

Status

approved