A135068 a(n) = [x^(2^n+n-1)] (x + x^2 + x^4 + x^8 + ... + x^2^n)^n for n>=1.

1, 2, 6, 16, 90, 636, 5712, 34336, 537282, 5941780, 99729146, 1049982792, 23200347040, 293841338896, 5712436923000, 68827002466176, 2844850573581890, 53069160498788772, 1545326270301621838, 26021954987946879560, 1020860369624228471394, 19905401189634441143740, 605270985059438427438138, 11141784565490367848976336, 621465511993167908247508400, 14470690420043042111787089216, 548187222712632324159956010732, 11881058908943228840652007583056

Offset: 1

Author

Paul D. Hanna, Nov 17 2007

Keywords

• nonn

Crossrefs

Cf. A007178 (variant); A135069, A135070 (variant), A135071.

Programs

Mathematica

f[x_, n_] := (Sum[x^(2^k), {k, 0, n}])^n; Table[Coefficient[f[x, n], x^(2^n + n - 1)] , {n, 1, 20}] (* G. C. Greubel, Sep 22 2016 *)

PARI

a(n)=if(n<1,0,polcoeff(sum(j=0,n,x^(2^j)+O(x^(2^n+n)))^n,2^n+n-1))

Formula

a(n) = A135069(n)*n.

Extensions

a(15)-a(19) from Alois P. Heinz, Apr 29 2009

a(20)-a(22) from Max Alekseyev, Dec 03 2010

a(23)-a(28) from Max Alekseyev, Aug 31 2024