A135071 a(n) = [x^(2^n+n-2)] (x + x^2 + x^4 + x^8 + ... + x^(2^n))^n /(n*(n-1)/2) for n>=2.

1, 1, 3, 7, 40, 236, 1876, 9948, 147880, 1453960, 22015900, 208197540, 4313645260, 50025596492, 908013578304, 10257540119128, 410662921858728, 7157148265575464, 196798065310375948, 3119117728942974484, 117123479632632724204, 2164788189493906776364, 62917262965957689991564, 1107373183582759036993164, 59647207431378288643241916, 1329593013280581859290571836, 48482067282133360326936987936

Offset: 2

Author

Paul D. Hanna, Nov 17 2007

Keywords

• nonn

Crossrefs

Cf. A135068, A135069, A135070.

Programs

Mathematica

f[x_, n_] := (1/Binomial[n, 2])*(Sum[x^(2^k), {k, 0, n}])^n; Table[Coefficient[f[x, n], x^(2^n + n - 2)] , {n, 2, 10}] (* G. C. Greubel, Sep 22 2016 *)

PARI

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

Formula

a(n) = A135070(n) / (n(n-1)/2) for n>=2.

Extensions

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

a(20)-a(21) from Max Alekseyev, Jul 25 2009

a(22)-a(28) from Max Alekseyev, Aug 31 2024