A180435 a(n) = a(n-1)*2^n+n, a(0)=1.

1, 3, 14, 115, 1844, 59013, 3776838, 483435271, 123759429384, 63364827844617, 64885583712887818, 132885675443994251275, 544299726618600453222412, 4458903360459574912797999117, 73054672657769675371282417532942

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Formula

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

a(n+1) = ((a(n - 2) + 4*a(n - 1) + 4)*a(n) - 2*a(n - 1)^2 - 4*a(n)^2 + a(n - 2) - 4*a(n - 1))/(a(n - 2) - 2*a(n - 1)).

a(n) = 2^(n*(n+1)/2) + sum_{k=1..n} 2^( (n+k+1)*(n-k)/2 ) * k. - Max Alekseyev, Sep 05 2010

Mathematica

nxt[{n_, a_}]:={n+1, a*2^(n+1)+n+1}; Transpose[NestList[nxt, {0, 1}, 20]] [[2]] (* Harvey P. Dale, Apr 05 2015 *)

Prog

(PARI) a(n)=if(n<=0, 1, a(n-1)*2^n+n )

Crossrefs

Cf. A010842.

Sequence in context: A279429 A333797 A229113 * A256159 A122081 A007140

Adjacent sequences: A180432 A180433 A180434 * A180436 A180437 A180438

Keyword

nonn

Author

Georgi Guninski, Sep 05 2010

Extensions

Minor edits by N. J. A. Sloane, Sep 05 2010

Status

approved