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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
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);
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k] + If[i > n, 0, k b[n - i, i, k]]]];
T[n_, k_] := Sum[b[n, n, k - i] (-1)^i/(i! (k - i)!), {i, 0, k}];
Table[T[n, 8], {n, 8, 30}] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)
CROSSREFS
Column k=8 of A256130.
Cf. A320550.
Sequence in context: A282927 A220684 A225971 * A320551 A211834 A216439
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 30 2015
STATUS
approved

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Last modified July 22 16:55 EDT 2024. Contains 374540 sequences. (Running on oeis4.)