A292462 Number of partitions of n with n sorts of part 1.

1, 1, 5, 31, 278, 3287, 48256, 843567, 17081639, 392869430, 10112244792, 287927207846, 8984122319997, 304828239096197, 11173376516829974, 439988449921648076, 18523908107054523591, 830292183207722271065, 39475390430795389762048, 1984220622132901208082220

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..386

Formula

a(n) = [x^n] 1/(1-n*x) * Product_{j=2..n} 1/(1-x^j).

a(n) ~ n^n * (1 + 1/n^2 + 1/n^3 + 2/n^4 + 2/n^5 + 4/n^6 + 4/n^7 + 7/n^8 + 8/n^9 + 12/n^10), for coefficients see A002865. - Vaclav Kotesovec, Sep 19 2017

a(n) = Sum_{j=0..n} A002865(j) * n^(n-j). - Alois P. Heinz, Sep 22 2017

Example

a(2) = 5: 2, 1a1a, 1a1b, 1b1a, 1b1b.

Maple

b:= proc(n, i, k) option remember; `if`(n=0 or i=1, k^n,
      `if`(i>n, 0, b(n-i, i, k))+b(n, i-1, k))
    end:
a:= n-> b(n$3):
seq(a(n), n=0..23);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0 || i == 1, k^n, If[i > n, 0, b[n - i, i, k]] + b[n, i - 1, k]];
a[0] = 1; a[n_] := b[n, n, n];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, May 19 2018, translated from Maple *)

Crossrefs

Cf. A002865, A246935, A292463, A292503, A292507, A292567.

Main diagonal of A292741.

Sequence in context: A218679 A296967 A347416 * A340392 A360774 A176302

Adjacent sequences: A292459 A292460 A292461 * A292463 A292464 A292465

Keyword

nonn

Author

Alois P. Heinz, Sep 16 2017

Status

approved