A062263 Sixth (unsigned) column of triangle A062140 (generalized a=4 Laguerre).

1, 60, 2310, 73920, 2162160, 60540480, 1664863200, 45664819200, 1261490630400, 35321737651200, 1006669523059200, 29284931579904000, 871226714502144000, 26538906072526848000, 828392996692445184000

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.: N(4;5, x)/(1-x)^15, with N(4;5, x) := Sum_{k=0..5} A062264(5, k)* x^k = 1 + 45*x + 360*x^2 + 840*x^3 + 630*x^4 + 226*x^5.

a(n) = A062140(n+5, 5).

a(n) = (n+5)!*binomial(n+9, 9)/5!.

If we define f(n,i,x) = Sum_{k=i..n} Sum_{j=i..k} binomial(k,j) * Stirling1(n,k) * Stirling2(j,i) * x^(k-j) then a(n-9) = (-1)^(n-1)*f(n,9,-6), (n>=9). - Milan Janjic, Mar 01 2009

Mathematica

Table[(n+5)!*Binomial[n+9, 9]/5!, {n, 0, 20}] (* _G. c. Greubel_, May 12 2018 *)

Prog

(PARI) { f=24; for (n=0, 100, f*=n + 5; write("b062263.txt", n, " ", f*binomial(n + 9, 9)/120) ) } \\ Harry J. Smith, Aug 03 2009
(Magma) [Factorial(n+5)*Binomial(n+9, 9)/Factorial(5): n in [0..20]]; // G. C. Greubel, May 12 2018

Crossrefs

Cf. A001720, A062140, A062199, A062260, A062261, A062262.

Sequence in context: A054623 A075908 A130647 * A075917 A058929 A057848

Adjacent sequences: A062260 A062261 A062262 * A062264 A062265 A062266

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 19 2001

Status

approved