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A258460 Number of partitions of n into parts of exactly 5 sorts which are introduced in ascending order. 4
1, 16, 157, 1223, 8331, 52078, 307122, 1738441, 9552809, 51357781, 271624053, 1418856775, 7341440755, 37708531955, 192586153199, 979219591861, 4961598056587, 25071026497266, 126410385360189, 636282269208285, 3198360708483673, 16059685003763157 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 5..1000

FORMULA

a(n) ~ c * 5^n, where c = 1/(5!*Product_{n>=1} (1-1/5^n)) = 1/(5!*QPochhammer[1/5, 1/5]) = 1/(5!*A100222) = 0.0109601129644612101609007882... . - 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, 5):

seq(a(n), n=5..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}];

a[n_] := T[n, 5];

Table[a[n], {n, 5, 30}] (* Jean-Fran├žois Alcover, May 22 2018, translated from Maple *)

CROSSREFS

Column k=5 of A256130.

Cf. A320547.

Sequence in context: A173763 A155649 A184598 * A320548 A211831 A036973

Adjacent sequences:  A258457 A258458 A258459 * A258461 A258462 A258463

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 30 2015

STATUS

approved

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Last modified November 18 17:45 EST 2019. Contains 329287 sequences. (Running on oeis4.)