A062261 -id:A062261 - cp's OEIS frontend

A062262 Fifth (unsigned) column sequence of triangle A062140 (generalized a=4 Laguerre).

1, 45, 1350, 34650, 831600, 19459440, 454053600, 10702692000, 256864608000, 6307453152000, 158947819430400, 4118193503424000, 109818493424640000, 3015784780968960000, 85303626661693440000

Offset: 0

Wolfdieter Lang, Jun 19 2001

Harry J. Smith, Table of n, a(n) for n = 0..100
Index entries for sequences related to Laguerre polynomials

Cf. A001720, A062199, A062260, A062261.

[Factorial(n+4)*Binomial(n+8,8)/24: n in [0..30]]; // G. C. Greubel, May 13 2018

Table[(n+4)!*Binomial[n+8, 8]/4!, {n, 0, 30}] (* G. C. Greubel, May 13 2018 *)
With[{nn=20},CoefficientList[Series[(1+32x+168x^2+224x^3+70x^4)/(1-x)^13,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 18 2025 *)

{ f=6; for (n=0, 100, f*=n + 4; write("b062262.txt", n, " ", f*binomial(n + 8, 8)/24) ) } \\ Harry J. Smith, Aug 03 2009

E.g.f.: (1+32*x+168*x^2+224*x^3+70*x^4)/(1-x)^13.
a(n) = A062140(n+4, 4).
a(n) = (n+4)!*binomial(n+8, 8)/4!.
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-4) = (-1)^n*f(n,4,-9), (n>=4). - Milan Janjic, Mar 01 2009

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

Original entry on oeis.org

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

Offset: 0

Wolfdieter Lang, Jun 19 2001

Harry J. Smith, Table of n, a(n) for n = 0..100
Index entries for sequences related to Laguerre polynomials

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

[Factorial(n+5)*Binomial(n+9, 9)/Factorial(5): n in [0..20]]; // G. C. Greubel, May 12 2018

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

{ 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

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

cp's OEIS Frontend

A062262 Fifth (unsigned) column sequence of triangle A062140 (generalized a=4 Laguerre).

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