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A258463 Number of partitions of n into parts of exactly 8 sorts which are introduced in ascending order. 3
1, 37, 788, 12705, 172520, 2084836, 23169639, 241881526, 2406802476, 23064505721, 214505275665, 1947297442670, 17332491414616, 151788374231505, 1311496639250495, 11205023121304298, 94832831557086797, 796244028801983324, 6640545376656071546 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 8..1000

FORMULA

a(n) ~ c * 8^n, where c = 1/(8!*Product_{n>=1} (1-1/8^n)) = 1/(8!*QPochhammer[1/8, 1/8]) = 0.0000288589880256565005640019500910465339603... . - Vaclav Kotesovec, Jun 01 2015

MAPLE

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

      b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k))))

    end:

T:= (n, k)-> add(b(n$2, k-i)*(-1)^i/(i!*(k-i)!), i=0..k):

a:= n-> T(n, 8):

seq(a(n), n=8..30);

CROSSREFS

Column k=8 of A256130.

Cf. A320550.

Sequence in context: A282927 A220684 A225971 * A320551 A211834 A216439

Adjacent sequences:  A258460 A258461 A258462 * A258464 A258465 A258466

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 30 2015

STATUS

approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)