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
Keywords
Examples
G.f. = 1 + 2*x + 5*x^2 + 23*x^3 + 156*x^4 + 1381*x^5 + 15035*x^6 + ...
Links
- Indranil Ghosh, Table of n, a(n) for n = 0..403
Programs
-
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
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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 *) -
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))};