A259900 n*a(n+1) = (2*n^2 + 3*n + 2)*a(n) - (n^2 - n - 2)*a(n-1) with n>1, a(0)=0, a(1)=1.

0, 1, 7, 56, 532, 5978, 78190, 1171016, 19795048, 373150316, 7765117444, 176867001920, 4377593349808, 117008560148984, 3359391916968808, 103116666783684512, 3370015324850779360, 116837927866976317904, 4283225196844255657072, 165548433805933065663104

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..403

Formula

a(n) ~ 7 * exp(1/4) * 2^(n+3) * n! * n^(1/4) / (15*Gamma(1/4)). - Vaclav Kotesovec, Jul 09 2015

Maple

f:= gfun:-rectoproc({n*a(n+1) = (2*n^2 + 3*n + 2)*a(n) - (n^2 - n - 2)*a(n-1), a(0)=0, a(1)=1}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Jan 29 2018

Mathematica

RecurrenceTable[{a[0] == 0, a[1] == 1, n a[n + 1] == (2 n^2 + 3 n + 2) a[n] - (n + 1) (n - 2) a[n - 1]}, a, {n, 30}]

Crossrefs

Sequence in context: A082305 A144263 A001730 * A087751 A099345 A245249

Adjacent sequences: A259897 A259898 A259899 * A259901 A259902 A259903

Keyword

nonn,easy

Author

G. C. Greubel, Jul 07 2015

Status

approved