A262718 a(n) = (n+1)^n - 2*(n^n) + (n-1)^n.

0, 0, 2, 18, 194, 2550, 39962, 730002, 15257090, 359376750, 9424209002, 272385029466, 8604312602690, 294957765448710, 10906288759973882, 432701819402940450, 18336112083960655874, 826578941145375829470, 39497618599385891373002, 1994276034034710498109674

Offset: 0

Author

Vladimir Kruchinin, Sep 28 2015

Keywords

• nonn
• easy

Comments

Obviously, a(n) is always an even number. - Altug Alkan, Sep 28 2015

Crossrefs

Cf. A000169, A000312, A062024.

Programs

Magma

[(n+1)^n - 2*(n^n) + (n-1)^n: n in [0..30]]; // Vincenzo Librandi, Sep 28 2015

Mathematica

Join[{0}, Table[(n + 1)^n - 2 (n^n) + (n - 1)^n, {n, 30}]] (* Vincenzo Librandi, Sep 28 2015 *)

Maxima

B(x):=-lambert_w(-x);
makelist(n!*coeff(taylor(diff(B(x),x)*(1-x/B(x))^2,x,0,20),x,n),n,0,10);

PARI

a(n) = (n+1)^n - 2*(n^n) + (n-1)^n;
vector(30, n, a(n-1)) \\ Altug Alkan, Sep 28 2015

Formula

E.g.f.: A(x) = B'(x)*(1-x/B(x))^2, where B(x) is g.f. of A000169.

a(n) = Sum{k=1..n} (k!*binomial(n-1,k-2)*stirling2(n,k)), n>0, a(0)=0.

a(n) = 2*(A062024(n) - A000312(n)). - Michel Marcus, Sep 28 2015