0,2

a(n) is also the number of ways of placing n labeled balls into 9 indistinguishable boxes and one special box, where the first ball is allowed to be member of the special box only if n=1.

a(n) = Sum_{m=0..n-1} C(n-1,m) Sum_{k=0..9} S2 (n-m, k), if n>1; a(n) = n+1 else.

a(n) = 2119/11520*2^n +103/840*3^n +53/1152*4^n +11/900*5^n +6^n/384 +7^n/2520 +8^n/11520 +10^n/403200, if n>1; a(n) = n+1 else.

G.f.: (403200*x^9 -478089*x^8 +35157*x^7 +202072*x^6 -136061*x^5 +42574*x^4 -7538*x^3 +774*x^2 -43*x+1) / ((2*x-1)* (3*x-1)* (4*x-1)* (5*x-1)* (6*x-1)* (7*x-1)* (8*x-1)* (10*x-1)).

a(0) = 1, the only possible word structure is the empty word.

a(1) = 2, word structures are a and X, where X denotes the special character.

a(2) = 3, word structures are aa, ab, aX.

a(3) = 10, word structures are aaa, aab, aba, baa, abc, aaX, abX, aXa, aXb, aXX.

# 1st program:

a:= n-> `if` (n<2, n+1, 2119/11520*2^n +103/840*3^n +53/1152*4^n +11/900*5^n +6^n/384 +7^n/2520 +8^n/11520 +10^n/403200): seq (a(n), n=0..30);

# 2nd program:

with (combinat): a:= n-> `if` (n<2, n+1, add (add (stirling2 (n-m, k), k=0..9) *binomial (n-1, m), m=0..n-1)): seq (a(n), n=0..30);

Cf. A007318, A048993, A164863, A164864, A000079, A000244, A007582, A086444, A005493, A138378.

Sequence in context: A060604 A141102 A144720 this_sequence A003048 A008980 A064183

Adjacent sequences: A164930 A164931 A164932 this_sequence A164934 A164935 A164936

easy,nonn

Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 31 2009