A167449 a(0)=1; a(1)=1; for a>1, a(n)=a(n-1)+((n-1)^3)*a(n-2).

1, 1, 2, 10, 64, 704, 8704, 160768, 3146240, 85459456, 2379068416, 87838524416, 3254378586112, 155039348776960, 7304909102465024, 432732882146443264, 25086801102965899264, 1797560686374797508608, 125049014505246260592640

Offset: 0

Author

Matthew Vandermast, Nov 09 2009

Keywords

• nonn

Comments

For n>0, a(n+1)=A166469(A167448(n)).

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..321

Crossrefs

Other sequences for which a(n)=a(n-1)+((n-1)^k)*a(n-2) are (k=0) A000045, (k=1) A000085, (k=2) A000142.

Programs

Mathematica

RecurrenceTable[{a[n] == a[n-1] + (n-1)^3*a[n-2], a[0] == 1, a[1] == 1}, a, {n, 0, 20}] (* Vaclav Kotesovec, Aug 08 2021 *)
nxt[{n_,a_,b_}]:={n+1,b,b+n^3 a}; NestList[nxt,{1,1,1},20][[;;,2]] (* Harvey P. Dale, Jan 22 2024 *)

Formula

a(n) ~ (c1 + c2*(-1)^n) * n^(3*n/2) / exp(3*n/2), where c1 = 11.229547293548917938785936532203403620187829245793... and c2 = -0.20385401969014506196353281640163785658756407221649... - Vaclav Kotesovec, Aug 10 2021