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A062148 Second (unsigned) column sequence of triangle A062138 (generalized a=5 Laguerre). 6
1, 14, 168, 2016, 25200, 332640, 4656960, 69189120, 1089728640, 18162144000, 319653734400, 5928123801600, 115598414131200, 2365321396838400, 50685458503680000, 1135354270482432000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..400

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Index entries for sequences related to Laguerre polynomials

FORMULA

E.g.f.: (1+6*x)/(1-x)^8.

a(n) = A062138(n+1, 1) = (n+1)!*binomial(n+6, 6).

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-1) = (-1)^(n-1) * f(n,1,-7), (n>=1). - Milan Janjic, Mar 01 2009

Assuming offset 1: a(n) = n!*binomial(-n,6). - Peter Luschny, Apr 29 2016

EXAMPLE

a(3) = (3+1)! * binomial(3+6,6) = 24 * 84 = 2016. - Indranil Ghosh, Feb 24 2017

MATHEMATICA

Table[Sum[n!/6!, {i, 6, n}], {n, 6, 21}] (* Zerinvary Lajos, Jul 12 2009 *)

PROG

(PARI) a(n)=(n+1)!*binomial(n+6, 6) \\ Indranil Ghosh, Feb 24 2017

(Python)

import math

f=math.factorial

def C(n, r):return f(n)/f(r)/f(n-r)

def A062148(n): return f(n+1)*C(n+6, 6) # Indranil Ghosh, Feb 24 2017

(MAGMA) [Factorial(n+1)*Binomial(n+6, 6): n in [0..30]]; // G. C. Greubel, Feb 06 2018

CROSSREFS

Cf. A001725 (first column of A062138).

Appears in the third left hand column of A167556 multiplied by 120. - Johannes W. Meijer, Nov 12 2009

Sequence in context: A273587 A125449 A159738 * A200164 A199529 A098299

Adjacent sequences:  A062145 A062146 A062147 * A062149 A062150 A062151

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jun 19 2001

STATUS

approved

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Last modified September 21 07:08 EDT 2019. Contains 327253 sequences. (Running on oeis4.)