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A285920
Number of ordered set partitions of [n] into five blocks such that equal-sized blocks are ordered with increasing least elements.
3
1, 75, 1225, 15750, 152355, 1049895, 8130925, 51541050, 305751160, 1721589870, 10370592050, 54481859250, 292852136335, 1539187989915, 8149972381105, 43456591157700, 220640087499230, 1133640238666320, 5822084961637780, 29811110400741780, 154396823960132126
OFFSET
5,2
LINKS
MAPLE
b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
(p+n)!/n!*x^n, add(x^j*b(n-i*j, i-1, p+j)*combinat
[multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i)), x, 6)
end:
a:= n-> coeff(b(n$2, 0), x, 5):
seq(a(n), n=5..30);
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, p_] := b[n, i, p] = Series[If[n == 0 || i == 1, (p + n)!/n!*x^n, Sum[x^j*b[n - i*j, i - 1, p + j]*multinomial[n, Join[{n - i*j}, Table[i, j]]]/j!^2, {j, 0, n/i}]], {x, 0, 6}];
a[n_] := Coefficient[b[n, n, 0], x, 5];
Table[a[n], {n, 5, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)
CROSSREFS
Column k=5 of A285824.
Cf. A285856.
Sequence in context: A264673 A320618 A218094 * A293581 A210047 A210505
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 28 2017
STATUS
approved