A062260 Third (unsigned) column sequence of triangle A062140 (generalized a=4 Laguerre).

1, 21, 336, 5040, 75600, 1164240, 18627840, 311351040, 5448643200, 99891792000, 1917922406400, 38532804710400, 809188898918400, 17739910476288000, 405483668029440000, 9650511299100672000

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+12*x+15*x^2)/(1-x)^9.

a(n) = A062140(n+2, 2) = (n+2)!*binomial(n+6, 6)/2!.

If we define f(n,i,x) = Sum_{k=1..n} Sum_{j=i..k} binomial(k,j) * Stirling1(n,k) * Stirling2(j,i) * x^(k-j) then a(n-2) = (-1)^n * f(n,2,-7), (n>=2). - Milan Janjic, Mar 01 2009

a(n) = binomial(n,6)*(n-4)!/2, n >= 6. - Zerinvary Lajos, Jul 07 2009

Maple

a:=n->sum((n-j)*n!/6!, j=5..n): seq(a(n), n=6..21); # Zerinvary Lajos, Apr 29 2007

Mathematica

Table[(n + 2)! Binomial[n + 6, 6]/2, {n, 0, 20}] (* Wesley Ivan Hurt, Jan 23 2017 *)

Prog

(Sage) [binomial(n, 6)*factorial (n-4)/2 for n in range(6, 22)] # Zerinvary Lajos, Jul 07 2009
(PARI) { f=1; for (n=0, 100, f*=n + 2; write("b062260.txt", n, " ", f*binomial(n + 6, 6)/2) ) } \\ Harry J. Smith, Aug 03 2009
(Magma) [Factorial(n+2)*Binomial(n+6, 6)/2: n in [0..30]]; // G. C. Greubel, Feb 06 2018

Crossrefs

Cf. A001720, A062199.

Sequence in context: A107396 A036224 A113895 * A278804 A166914 A020311

Adjacent sequences: A062257 A062258 A062259 * A062261 A062262 A062263

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 19 2001

Status

approved