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A305966 Number of length-n restricted growth strings (RGS) with growth <= six and fixed first element. 3
1, 1, 7, 70, 875, 12887, 216552, 4065775, 84022595, 1889844292, 45857269017, 1191971998455, 32996489835190, 968034453578997, 29972909437783507, 975944207096597110, 33313664777283768535, 1188852507118147925627, 44246989258071738375272, 1713739685432232160181115 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..432

FORMULA

a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..6} (exp(j*x)-1)/j) for n>0, a(0) = 1.

MAPLE

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

      add(b(n-1, max(m, j)), j=1..m+6))

    end:

a:= n-> b(n, -5):

seq(a(n), n=0..25);

# second Maple program:

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

           (exp(j*x)-1)/j, j=1..6)), x, n), x, n-1)):

seq(a(n), n=0..25);

CROSSREFS

Column k=6 of A305962.

Cf. A306030.

Sequence in context: A027394 A209327 A255519 * A226805 A113343 A124566

Adjacent sequences:  A305963 A305964 A305965 * A305967 A305968 A305969

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 15 2018

STATUS

approved

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Last modified November 12 14:42 EST 2019. Contains 329058 sequences. (Running on oeis4.)