A203641 Number of arrays of n 0..10 integers with new values introduced in order 0..10 but otherwise unconstrained.

1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213596, 27644358, 190895863, 1382847419, 10477213268, 82797679445, 680685836527, 5806124780384, 51245294979716, 466668627500968, 4371727233798927, 42000637216351225

Offset

1,2

Comments

From Danny Rorabaugh, Mar 03 2015: (Start)

a(n) is also the number of ways of placing n labeled balls into 11 indistinguishable boxes.

a(n) is also the number of word structures of length n using an 11-ary alphabet.

(End)

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Eric Weisstein's World of Mathematics, Set Partition.

Formula

Empirical: a(n) = 56*a(n-1) -1365*a(n-2) +19020*a(n-3) -167223*a(n-4) +965328*a(n-5) -3686255*a(n-6) +9133180*a(n-7) -13926276*a(n-8) +11655216*a(n-9) -3991680*a(n-10).

a(n) = Sum_{k=1..11} stirling2(n,k). - Danny Rorabaugh, Mar 03 2015

G.f.: Sum_{k=1..11} Product_{j=1..k} x/(1-j*x). This confirms the empirical recurrence. - Robert Israel, Aug 08 2016

Maple

f:= n -> add(Stirling2(n, k), k=1..11):
map(f, [$1..100]); # Robert Israel, Aug 08 2016

Prog

(PARI) a(n) = sum(k=1, 11, stirling(n, k, 2)); \\ Michel Marcus, Mar 03 2015

Crossrefs

Column k=10 of A203647.

Cf. A056272, A056273, A164863, A164864.

Sequence in context: A287282 A287260 A287672 * A192127 A287673 A203642

Adjacent sequences: A203638 A203639 A203640 * A203642 A203643 A203644

Keyword

nonn,easy

Author

R. H. Hardin, Jan 04 2012

Status

approved