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A285919 Number of ordered set partitions of [n] into four blocks such that equal-sized blocks are ordered with increasing least elements. 3
1, 40, 350, 3080, 17129, 82488, 464650, 1901680, 8357426, 35701952, 159721016, 627687060, 2642405289, 10712590392, 45568675202, 178738923440, 736145997686, 2946913512648, 12311241803256, 48275516469180, 197284995875314, 786939537437440, 3254422571085400 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,2
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, 5)
end:
a:= n-> coeff(b(n$2, 0), x, 4):
seq(a(n), n=4..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, 5}];
a[n_] := Coefficient[b[n, n, 0], x, 4];
Table[a[n], {n, 4, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)
CROSSREFS
Column k=4 of A285824.
Cf. A285855.
Sequence in context: A365607 A247407 A251431 * A234913 A190312 A229532
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 28 2017
STATUS
approved

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Last modified March 4 05:23 EST 2024. Contains 370522 sequences. (Running on oeis4.)