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A305963 Number of length-n restricted growth strings (RGS) with growth <= n and fixed first element. 3
1, 1, 3, 22, 305, 6756, 216552, 9416240, 530764089, 37498693555, 3235722405487, 334075729235172, 40587204883652869, 5722676826879812177, 925590727478445526747, 170032646641380554970304, 35173161711207720944899921, 8132124409499796317194563900 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..266

FORMULA

a(n) = (n-1)! * [x^(n-1)] exp(x + Sum_{j=1..n} (exp(j*x)-1)/j) for n > 0, a(0) = 1.

a(n) = A305962(n,n).

EXAMPLE

a(2) = 3: 11, 12, 13.

a(3) = 22: 111, 112, 113, 114, 121, 122, 123, 124, 125, 131, 132, 133, 134, 135, 136, 141, 142, 143, 144, 145, 146, 147.

MAPLE

b:= proc(n, k, m) option remember; `if`(n=0, 1,

      add(b(n-1, k, max(m, j)), j=1..m+k))

    end:

a:= n-> b(n$2, 1-n):

seq(a(n), n=0..20);

# second Maple program:

a:= n-> `if`(n=0, 1, (n-1)!*coeff(series(exp(x+add(

           (exp(j*x)-1)/j, j=1..n)), x, n), x, n-1)):

seq(a(n), n=0..20);

CROSSREFS

Main diagonal of A305962.

Cf. A306025.

Sequence in context: A119390 A271848 A144681 * A261280 A124567 A161967

Adjacent sequences:  A305960 A305961 A305962 * A305964 A305965 A305966

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 15 2018

STATUS

approved

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Last modified October 22 18:45 EDT 2021. Contains 348175 sequences. (Running on oeis4.)