A142722 - OEIS

A142722

a(0)=a(1)=1 and a(n) = -(2*n-1)*a(n-1) + a(n-2) for n>=2.

1, 1, -2, 11, -79, 722, -8021, 104995, -1582946, 27015077, -514869409, 10839272666, -249818140727, 6256292790841, -169169723493434, 4912178274100427, -152446696220606671, 5035653153554120570, -176400307070614826621, 6531847014766302705547

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

MAPLE

a:= proc(n) if n<2 then 1 else a(n) := -(2*n-1)*a(n-1) + a(n-2) fi end:

seq (a(n), n=0..25); # Sergei N. Gladkovskii, Jul 04 2012

MATHEMATICA

k = 2; b[0] = 1; b[n_] := b[n] = b[n - 1] + k

M[0] := {{-b[n], -1}, {1, 0}};

M[1] := {{-b[n], 1}, {-1, 0}};

v[0] = {1, 1};

v[n_] := v[n] = M[Mod[n, 2]].v[n - 1];

Table[v[n][[1]], {n, 1, 30}]

RecurrenceTable[{a[0]==a[1]==1, a[n]==-(2n-1)a[n-1]+a[n-2]}, a, {n, 20}] (* Harvey P. Dale, May 08 2019 *)

PROG

(PARI)

a(n)= if ( n<=1, 1, -(2*n-1)*a(n-1) + a(n-2) );

/* note this is inefficient, optimize using memoization: */

v=vector(66); v[1]=1; v[2]=1; /* PARI's vectors are one-based */

for (n=3, #v, v[n] = -(2*n-3)*v[n-1] + v[n-2]);

v /* show terms */

/* Joerg Arndt, Jul 023 2012 */

CROSSREFS

Sequence in context: A154273 A253256 A163203 * A320095 A099661 A027110

Adjacent sequences: A142719 A142720 A142721 * A142723 A142724 A142725

KEYWORD

sign

AUTHOR

Roger L. Bagula and Gary W. Adamson, Sep 27 2008

STATUS

approved