A059604 -id:A059604 - cp's OEIS frontend

A059605 a(n) = (1/3!)(n^3 + 24n^2 + 107*n + 90), compare A059604.

15, 37, 68, 109, 161, 225, 302, 393, 499, 621, 760, 917, 1093, 1289, 1506, 1745, 2007, 2293, 2604, 2941, 3305, 3697, 4118, 4569, 5051, 5565, 6112, 6693, 7309, 7961, 8650, 9377, 10143, 10949, 11796, 12685, 13617, 14593, 15614, 16681, 17795, 18957

Offset: 0

Vladeta Jovovic, Jan 29 2001

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
More information

Cf. A052905, A059340, A059604, A059606.

[(1/6)*(n^3+24*n^2+107*n+90) : n in [0..50]]; // Vincenzo Librandi, Nov 13 2011

G.f.: (15 - 23*x + 10*x^2 - x^3)/(1-x)^4, compare A059340.

More terms from James Sellers, Feb 01 2001

A059606 Expansion of (1/2)(exp(2x)-1)*exp(exp(x)-1).

Original entry on oeis.org

0, 1, 4, 16, 68, 311, 1530, 8065, 45344, 270724, 1709526, 11376135, 79520644, 582207393, 4453142140, 35500884556, 294365897104, 2533900264547, 22604669612078, 208656457858161, 1990060882027600

Offset: 0

Vladeta Jovovic, Jan 29 2001

Starting (1, 4, 16, 68, 311, ...), = A008277 * A000217, i.e., the product of the Stirling2 triangle and triangular series. - Gary W. Adamson, Jan 31 2008

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Vladeta Jovovic, More information.

Cf. A000110, A005493, A059604, A059605.
Cf. A035098.
Cf. A008277, A000217.

s := series(1/2*(exp(2*x)-1)*exp(exp(x)-1), x, 21): for i from 0 to 20 do printf(`%d,`,i!*coeff(s,x,i)) od:

With[{nn=20},CoefficientList[Series[((Exp[2x]-1)Exp[Exp[x]-1])/2,{x,0,nn}] ,x] Range[0,nn]!] (* Harvey P. Dale, Nov 10 2011 *)

a(n) = Sum_{i=0..n} Stirling2(n, i)*binomial(i+1, 2).
a(n) = (1/2)*(Bell(n+2)-Bell(n+1)-Bell(n)). - Vladeta Jovovic, Sep 23 2003
G.f.: Sum_{k>=1} (k*(k + 1)/2)*x^k/Product_{j=1..k} (1 - j*x). - Ilya Gutkovskiy, Jun 19 2018
a(n) ~ n^2 * Bell(n) / (2*LambertW(n)^2) * (1 - LambertW(n)/n). - Vaclav Kotesovec, Jul 28 2021

cp's OEIS Frontend

A059605 a(n) = (1/3!)(n^3 + 24n^2 + 107*n + 90), compare A059604.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Formula

Extensions

A059606 Expansion of (1/2)(exp(2x)-1)*exp(exp(x)-1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Formula

cp's OEIS Frontend

A059605 a(n) = (1/3!)*(n^3 + 24*n^2 + 107*n + 90), compare A059604.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Formula

Extensions

A059606 Expansion of (1/2)*(exp(2*x)-1)*exp(exp(x)-1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A059605 a(n) = (1/3!)(n^3 + 24n^2 + 107*n + 90), compare A059604.

A059606 Expansion of (1/2)(exp(2x)-1)*exp(exp(x)-1).