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A258474 Number of partitions of n into two sorts of parts having exactly 4 parts of the second sort. 2
1, 6, 22, 63, 155, 342, 700, 1343, 2463, 4323, 7361, 12139, 19581, 30819, 47697, 72388, 108390, 159752, 232833, 334917, 477270, 672589, 940222, 1301954, 1790117, 2441168, 3308341, 4451294, 5955870, 7918574, 10475192, 13779096, 18042899, 23506156, 30496836 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

LINKS

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

MAPLE

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

      `if`(i<1, 0, add(b(n-i*j, i-1)*add(x^t*

       binomial(j, t), t=0..min(4, j)), j=0..n/i))), x, 5)

    end:

a:= n-> coeff(b(n$2), x, 4):

seq(a(n), n=4..40);

MATHEMATICA

b[n_, i_] := b[n, i] = Series[If[n==0, 1, If[i<1, 0, Sum[b[n-i*j, i-1]*Sum[ x^t*Binomial[j, t], {t, 0, Min[4, j]}], {j, 0, n/i}]]], {x, 0, 5}];

a[n_] := Coefficient[b[n, n], x, 4];

a /@ Range[4, 40] (* Jean-Fran├žois Alcover, Dec 11 2020, after Alois P. Heinz *)

CROSSREFS

Column k=4 of A256193.

Sequence in context: A166020 A307621 A257200 * A120477 A053739 A280481

Adjacent sequences:  A258471 A258472 A258473 * A258475 A258476 A258477

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 31 2015

STATUS

approved

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Last modified May 23 12:44 EDT 2022. Contains 353975 sequences. (Running on oeis4.)