A188387 Central coefficient in (1 + (2^n+1)*x + 2^n*x^2)^n for n>=0.

1, 3, 33, 1161, 140545, 63148833, 111254837505, 793938286762113, 23282575640347295745, 2812444483776375381074433, 1393909730376211388561041231873

Offset: 0

Author

Paul D. Hanna, Mar 29 2011

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..36

Crossrefs

Cf. A187021.

Programs

Magma

/*1*/ P:=PolynomialRing(Integers()); [ Coefficients((1+(2^n+1)*x+2^n*x^2)^n)[n+1]: n in [0..10] ]; /*2*/ &cat[ [&+[ Binomial(n, k)^2*2^(n*k): k in [0..n]]]: n in [0..10] ]; // Bruno Berselli, Mar 30 2011

Mathematica

Table[Sum[Binomial[n,k]^2 * 2^(n*k), {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Feb 11 2015 *)

PARI

{a(n)=polcoeff((1+(2^n+1)*x+2^n*x^2+x*O(x^n))^n,n)}

PARI

{a(n)=sum(k=0,n,binomial(n,k)^2*2^(n*k))}

Formula

a(n) = Sum_{k=0..n} C(n,k)^2 * 2^(n*k).

a(n) ~ 2^(n^2). - Vaclav Kotesovec, Feb 12 2015