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# User:Georgi Guninski/seqs/A180435

${\displaystyle a_{n}=a_{n-1}2^{n}+n}$

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

## Contents

### Sequence

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

0,2

### 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 Alwekseyev, Sep 05 2010

${\displaystyle a_{n+1}={\left(2^{\left(n+1\right)}+1\right)}a_{n}-2^{n}a_{n-1}+1}$

${\displaystyle a_{n+1}={\frac {(a_{n-2}+4a_{n-1}+4)a_{n}-2a_{n-1}^{2}-4a_{n}^{2}+a_{n-2}-4a_{n-1}}{a_{n-2}-2a_{n-1}}}}$

${\displaystyle a_{n}=2^{\frac {n(n+1)}{2}}+\sum _{k=1}^{n}{{2^{\frac {(n+k+1)(n-k)}{2}}}k}}$

### Program

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