A176408 a(n) = (n+1)*(a(n-1) +a(n-2)) n>1, a(0)=1,a(1)=0.

1, 0, 3, 12, 75, 522, 4179, 37608, 376083, 4136910, 49642923, 645357996, 9035011947, 135525179202, 2168402867235, 36862848742992, 663531277373859, 12607094270103318

Offset: 0

Author

Gary Detlefs, Apr 16 2010

Keywords

• nonn

Comments

a(n) is one of two "basis" sequences for sequences of the form s(0)=a,s(1)=b,s(n)=(n+1)(s(n-1)+s(n-2)), n>1, the other being A006347.

s(n) = a*a(n) + b* A006347(n+1).

s(n) = 1/2*(b-2*a)(n+2)! +(3*a-b)*floor(((n+2)!+1)/e).

Examples

			a(2)= 3*9-24=3, a(3)= 3*44-120=12, a(4)= 3*265-720=75, ...
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..447
• Michael Wallner, A bijection of plane increasing trees with relaxed binary trees of right height at most one, arXiv:1706.07163 [math.CO], 2017, Table 2 on p. 13.

Crossrefs

Cf. A000166, A006347.

Programs

Maple

seq(3*floor(((n+2)!+1)/E) - (n+2)!,n=1..20);

Formula

a(n) = 3*floor(((n+2)!+1)/e) - (n+2)!.

a(n) = 3* A000166(n+1) - (n+2)!, where A000166 are the subfactorial numbers.

Extensions

Data section corrected by Indranil Ghosh, Feb 15 2017