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

0,5

Links

Table of n, a(n) for n=0..30.

Formula

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

Prog

(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)}

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)

Sequence in context: A238436 A366229 A137681 * A152173 A032171 A127713

Adjacent sequences: A127386 A127387 A127388 * A127390 A127391 A127392

Keyword

nonn

Author

Antti Karttunen, Jan 16 2007. Generating function, PARI-program and most of the terms supplied by Paul D. Hanna, Jan 15 2007.

Status

approved