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A258459 Number of partitions of n into parts of exactly 4 sorts which are introduced in ascending order. 4
1, 11, 77, 438, 2216, 10422, 46731, 202814, 860586, 3593561, 14834956, 60735095, 247155292, 1001318246, 4043482110, 16288762319, 65500024027, 263035832734, 1055252430510, 4230340216034, 16949359882259, 67881449170593, 271777855641517, 1087867649157513 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..1000

FORMULA

a(n) ~ c * 4^n, where c = 1/(24*Product_{n>=1} (1-1/4^n)) = 1/(24*QPochhammer[1/4, 1/4]) = 1/(24*A100221) = 0.060514735102066542326446... . - 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, 4):

seq(a(n), n=4..35);

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, 4], {n, 4, 35}] (* Jean-Fran├žois Alcover, May 25 2018, translated from Maple *)

CROSSREFS

Column k=4 of A256130.

Cf. A320546.

Sequence in context: A059625 A023010 A303103 * A320547 A022639 A000589

Adjacent sequences:  A258456 A258457 A258458 * A258460 A258461 A258462

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 30 2015

STATUS

approved

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Last modified February 16 15:17 EST 2020. Contains 331961 sequences. (Running on oeis4.)