A127389 Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutations A127377/A127378 and A127387.

1, 1, 0, 1, 2, 4, 10, 23, 56, 138, 344, 870, 2220, 5716, 14828, 38717, 101682, 268416, 711810, 1895432, 5066030, 13586082, 36547534, 98593064, 266661162, 722953814, 1964358938, 5348367006, 14589803090, 39870312218, 109136843138

Offset: 0

Author

Antti Karttunen, Jan 16 2007

Keywords

• nonn

Crossrefs

This is INVERTi transform of A086625 (appropriately shifted). I.e. INVERT([1, 1, 0, 1, 2, 4, 10, 23, 56, 138, 344, 870, 2220, 5716]) gives: 1, 2, 3, 6, 12, 26, 59, 138, 332, 814, 2028, 5118, ... (beginning of A086625)

Programs

PARI

{a(n)=local(A=1+x+x*O(x^n));for(i=0,n,A=(1 + x*A^2)*(1+x)/(1+x+2*x^2));polcoeff(A,n)}

Formula

G.f. satisfies: A(x) = (1 + x*A(x)^2)*(1+x)/(1+x+2*x^2).

Extensions

Generating function, PARI-program and most of the terms supplied by Paul D. Hanna, Jan 15 2007