A242227 a(n) = (2*n-1) * a(n-1) - a(n-2), a(0) = 1, a(1) = 2.

1, 2, 5, 23, 156, 1381, 15035, 194074, 2896075, 49039201, 928848744, 19456784423, 446577192985, 11144973040202, 300467694892469, 8702418178841399, 269474495849190900, 8883955944844458301, 310668983573706849635, 11485868436282308978194

Offset

0,2

Links

Indranil Ghosh, Table of n, a(n) for n = 0..403

Formula

a(n) = A053983(n) + A053984(n) = -(-1)^n * A121323(-2-n) for all integer n.

0 = a(n)*(a(n+2)) + a(n+1)*(-a(n+1) + 2*a(n+2) - a(n+3)) + a(n+2)*(a(n+2)) for all integer n.

Example

G.f. = 1 + 2*x + 5*x^2 + 23*x^3 + 156*x^4 + 1381*x^5 + 15035*x^6 + ...

Mathematica

RecurrenceTable[{a[n] == (2*n-1)*a[n-1] - a[n-2], a[0] == 1, a[1] == 2}, a, {n, 0, 50}] (* G. C. Greubel, Aug 06 2018 *)
nxt[{n_, a_, b_}]:={n+1, b, b(2n+1)-a}; NestList[nxt, {1, 1, 2}, 20][[All, 2]] (* Harvey P. Dale, Aug 01 2022 *)

Prog

(PARI) {a(n) = if( n>-4, if( n<0, -2-n, (2*n - 1) * a(n-1) - a(n-2)), (2*n + 3) * a(n+1) - a(n+2))};
(Magma) I:=[1, 2]; [n le 2 select I[n] else (2*n-1)*Self(n-1) - Self(n-2): n in [1..30]]; // G. C. Greubel, Aug 06 2018

Crossrefs

Cf. A053983, A053984, A121323.

Sequence in context: A003501 A006990 A358608 * A032182 A165902 A191600

Adjacent sequences: A242224 A242225 A242226 * A242228 A242229 A242230

Keyword

nonn

Author

Michael Somos, May 08 2014

Status

approved