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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, 1, 5, 151, 19025, 9702751, 19851828545, 162586475783551, 5327308465523832065, 698250320576208668759551, 366082867573618138109269955585, 767730685732013278335855487355082751, 6440190236715680978727827356359771295535105
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OFFSET
0,3
COMMENTS
A variant of
A005014
. Equals row sums (unsigned) of triangle
A214690
.
LINKS
Table of n, a(n) for n=0..12.
FORMULA
a(n) = 2*(4^(n-1) - 1)*a(n-1) - (-1)^n for n>0 with a(0)=1.
PROG
(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), ", "));
CROSSREFS
Cf.
A005014
(variant),
A214690
.
Sequence in context:
A332115
A262655
A075598
*
A261822
A105230
A222768
Adjacent sequences:
A214688
A214689
A214690
*
A214692
A214693
A214694
KEYWORD
nonn
AUTHOR
Paul D. Hanna
, Jul 26 2012
STATUS
approved
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Last modified April 23 15:20 EDT 2024. Contains 371916 sequences. (Running on oeis4.)