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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-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

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Last modified August 4 22:06 EDT 2024. Contains 374934 sequences. (Running on oeis4.)