A214691 G.f.: A(x) = Sum_{n>=0} x^n * Product_{k=1..n} (2^(2*k-1) - 1) / (1 + 2^(2*k-1)*x).

1, 1, 5, 151, 19025, 9702751, 19851828545, 162586475783551, 5327308465523832065, 698250320576208668759551, 366082867573618138109269955585, 767730685732013278335855487355082751, 6440190236715680978727827356359771295535105

Offset: 0

Author

Paul D. Hanna, Jul 26 2012

Keywords

• nonn

Comments

A variant of A005014. Equals row sums (unsigned) of triangle A214690.

Crossrefs

Cf. A005014 (variant), A214690.

Programs

PARI

{a(n)=if(n==0,1,2*(4^(n-1)-1)*a(n-1) - (-1)^n)}

PARI

{a(n)=local(A=x); A=sum(m=0, n, x^m*prod(j=1, m, (2^(2*j-1)-1)/(1+x*2^(2*j-1))+x*O(x^n))); polcoeff(A, n, x)}
for(n=0, 20, print1(a(n), ", "));

Formula

a(n) = 2*(4^(n-1) - 1)*a(n-1) - (-1)^n for n>0 with a(0)=1.