cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A027436 G.f. f(x) = Sum_{n>=1} a(n)*x^n satisfies f(f(x)) = x*(1 + 4*x).

Original entry on oeis.org

0, 1, 2, -4, 16, -80, 432, -2304, 10944, -35328, -74112, 2736384, -30853632, 238663680, -1247457280, 2201247744, 32530722816, -320650199040, 156266184704, 18314630348800, -20667999748096, -3428200020508672
Offset: 0

Views

Author

Jonathan Deane

Keywords

Links

Crossrefs

Cf. A097088, A097089.

Formula

a(n) = 4^(n-1) * A097088(n) / 2^A097089(n).
T(n,m) = if n=m then 1 else (binomial(m,n-m)*4^(n-m)-sum(i=m+1..n-1, T(n,i)*T(i,m)))/2. a(n) = T(n,1). - Vladimir Kruchinin, Nov 08 2011

Extensions

Added a(0)=0 (sum in title starts at a(1)), Henry Bottomley, Apr 20 2011

A097089 Exponents of 2 that form the denominators of coefficients in function A(x) such that A(A(x)) = x+x^2.

Original entry on oeis.org

0, 0, 1, 2, 2, 4, 6, 4, 8, 7, 11, 12, 13, 13, 14, 15, 18, 18, 20, 22, 23, 24, 26, 26, 25, 26, 30, 31, 33, 32, 34, 33, 38, 38, 39, 39, 42, 44, 46, 46, 46, 48, 51, 52, 53, 53, 55, 55, 56, 55, 59, 61, 62, 63, 65, 66, 68, 68, 70, 71, 73
Offset: 0

Views

Author

Paul D. Hanna, Jul 23 2004

Keywords

Comments

A097088 lists the reduced numerators.

Crossrefs

Cf. A097088.

Programs

  • PARI
    {a(n)=local(A,B,F=x+x^2+x*O(x^n));A=F; if(n==0,0, for(i=0,n,B=serreverse(A);A=(A+subst(B,x,F))/2); valuation(denominator(polcoeff(A,n,x)),2))}

Formula

G.f.: A(x) = Sum_{n>=0} A097088(n)/2^a(n) where A(A(x)) = x + x^2.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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