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 A258463 Number of partitions of n into parts of exactly 8 sorts which are introduced in ascending order. 3

%I #12 Dec 07 2020 14:00:32

%S 1,37,788,12705,172520,2084836,23169639,241881526,2406802476,

%T 23064505721,214505275665,1947297442670,17332491414616,

%U 151788374231505,1311496639250495,11205023121304298,94832831557086797,796244028801983324,6640545376656071546

%N Number of partitions of n into parts of exactly 8 sorts which are introduced in ascending order.

%H Alois P. Heinz, <a href="/A258463/b258463.txt">Table of n, a(n) for n = 8..1000</a>

%F 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

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

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

%p end:

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

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

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

%t 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 T[n_, k_] := Sum[b[n, n, k - i] (-1)^i/(i! (k - i)!), {i, 0, k}];

%t Table[T[n, 8], {n, 8, 30}] (* _Jean-François Alcover_, Dec 07 2020, after _Alois P. Heinz_ *)

%Y Column k=8 of A256130.

%Y Cf. A320550.

%K nonn

%O 8,2

%A _Alois P. Heinz_, May 30 2015

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Last modified August 13 17:42 EDT 2024. Contains 375144 sequences. (Running on oeis4.)