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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

• 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).

Crossrefs

Equals A000582 - 1. Cf. A014553, A179239.

Programs

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 *)

PARI

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

Formula

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