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 A092321 Sum of largest parts (counted with multiplicity) of all partitions of n. 12
 0, 1, 4, 8, 17, 26, 49, 69, 115, 164, 249, 343, 513, 686, 974, 1314, 1806, 2382, 3232, 4208, 5597, 7244, 9456, 12118, 15687, 19899, 25422, 32079, 40589, 50796, 63805, 79303, 98817, 122179, 151145, 185820, 228598, 279476, 341807, 416051, 506205, 613244, 742720 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Alois P. Heinz) Margaret Archibald, A. Blecher, C. Brennan, A. Knopfmacher and T. Mansour, Partitions according to multiplicities and part sizes, Australasian Journal of Combinatorics, Volume 66(1) (2016), Pages 104-119. Ljuben Mutafchiev, On the Largest Part Size and Its Multiplicity of a Random Integer Partition, arXiv:1712.03233 [math.PR], 2017. FORMULA G.f.: Sum_{n>=1} (n*x^n/(1-x^n))*Product_{k=1..n} 1/(1-x^k). EXAMPLE Partitions of 4 are [1,1,1,1], [1,1,2], [2,2], [1,3], [4]; thus a(4) = 4*1 + 1*2 + 2*2 + 1*3 + 1*4 = 17. MAPLE b:= proc(n, i, t) option remember; `if`(n=0, [1, 0],       `if`(i<1, [0\$2], b(n, i-1, t) +add((l->`if`(t, l,        l+[0, l[1]*i*j]))(b(n-i*j, i-1, true)), j=1..n/i)))     end: a:= n-> b(n\$2, false)[2]: seq(a(n), n=0..50);  # Alois P. Heinz, Jan 29 2014 MATHEMATICA f[n_] := Block[{c = 2n, k = 2, p = IntegerPartitions[n]}, m = Max @@@ p; l = Length[p]; While[k < l, c = c + m[[k]]*Count[p[[k]], m[[k]]]; k++ ]; If[n == 1, 1, c]]; Table[ f[n], {n, 41}] (* Robert G. Wilson v, Feb 18 2004, updated by Jean-François Alcover, Jan 29 2014 *) nmax = 50; CoefficientList[Series[Sum[n*x^n/(1-x^n) * Product[1/(1 - x^k), {k, 1, n}], {n, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 06 2019 *) Join[{0}, Table[Total[Flatten[First[Split[#]]&/@IntegerPartitions[n]]], {n, 50}]] (* Harvey P. Dale, Oct 29 2019 *) CROSSREFS Cf. A006128, A092314, A092322, A092269, A092309, A092313, A092310, A092311, A092268. Sequence in context: A345432 A298950 A213494 * A026353 A067773 A301145 Adjacent sequences:  A092318 A092319 A092320 * A092322 A092323 A092324 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Feb 16 2004 EXTENSIONS More terms from Robert G. Wilson v, Feb 18 2004 STATUS approved

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Last modified May 26 20:51 EDT 2022. Contains 354092 sequences. (Running on oeis4.)