A035927 One less than number of n-multisets chosen from a 10-set.

0, 9, 54, 219, 714, 2001, 5004, 11439, 24309, 48619, 92377, 167959, 293929, 497419, 817189, 1307503, 2042974, 3124549, 4686824, 6906899, 10015004, 14307149, 20160074, 28048799, 38567099, 52451255, 70607459, 94143279

Offset

0,2

Comments

Number of distinct n-digit numbers up to permutations of digits. - Michael Somos, Jul 11 2002

Equivalently, for n > 0, a(n) = number of n-digit decimal numbers d_1 d_2 ... d_n with d_1 > 0 and d_1 >= d_2 >= ... >= d_n >= 0.. - N. J. A. Sloane, Jul 13 2023

Links

Table of n, a(n) for n=0..27.

Michael Beeler, R. William Gosper and Richard C. Schroeppel, HAKMEM, ITEM 56, Cambridge, MA: Mass. Institute of Technology Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972, Item 56.

Eric Weisstein's World of Mathematics, Multiplicative Persistence.

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

G.f.: 1/(1-x)^10-1/(1-x). - Michael Somos, Jul 11 2002

Maple

binomial(10+n-1, n)-1;

Mathematica

Table[Binomial[9 + n, n] - 1, {n, 0, 27}] (* Michael De Vlieger, Jul 14 2015 *)
CoefficientList[Series[1/(1-x)^10-1/(1-x), {x, 0, 30}], x] (* or *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 9, 54, 219, 714, 2001, 5004, 11439, 24309, 48619}, 30] (* Harvey P. Dale, Jul 11 2023 *)

Prog

(PARI) a(n)=if(n<0, 0, binomial(n+9, 9)-1)

Crossrefs

Equals A000582 - 1. Cf. A014553, A179239.

Sequence in context: A073974 A223927 A307045 * A250286 A289254 A059597

Adjacent sequences: A035924 A035925 A035926 * A035928 A035929 A035930

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved