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A322296 Number of permutations of [2n+1] with exactly n rising or falling successions. 2
1, 4, 48, 888, 22120, 685368, 25344480, 1087931184, 53138966904, 2909014993080, 176372774697856, 11729862804913680, 848948339328178128, 66420006805308507568, 5585680154203107163200, 502437191145813112268640, 48134705092961286591532440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..347

FORMULA

a(n) = A001100(2n+1,n).

MAPLE

S:= proc(n) option remember; `if`(n<4, [1, 1, 2*t, 4*t+2*t^2]

       [n+1], expand((n+1-t)*S(n-1) -(1-t)*(n-2+3*t)*S(n-2)

       -(1-t)^2*(n-5+t)*S(n-3) +(1-t)^3*(n-3)*S(n-4)))

    end:

a:= n-> coeff(S(2*n+1), t, n):

seq(a(n), n=0..20);

CROSSREFS

Bisection (odd part) of A322294.

Cf. A001100.

Sequence in context: A047711 A089448 A167141 * A192260 A162676 A141119

Adjacent sequences:  A322293 A322294 A322295 * A322297 A322298 A322299

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 02 2018

STATUS

approved

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Last modified November 19 22:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)