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A292462 Number of partitions of n with n sorts of part 1. 6
1, 1, 5, 31, 278, 3287, 48256, 843567, 17081639, 392869430, 10112244792, 287927207846, 8984122319997, 304828239096197, 11173376516829974, 439988449921648076, 18523908107054523591, 830292183207722271065, 39475390430795389762048, 1984220622132901208082220 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, May 19 2018, translated from Maple *)

CROSSREFS

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

Main diagonal of A292741.

Sequence in context: A273601 A218679 A296967 * A340392 A176302 A129586

Adjacent sequences:  A292459 A292460 A292461 * A292463 A292464 A292465

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 16 2017

STATUS

approved

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Last modified August 4 21:32 EDT 2021. Contains 346455 sequences. (Running on oeis4.)