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 A242642 Triangle read by rows: T(s,n) (n>=1, 1 <= s <= n) = number of s-line partitions of n. 2
 1, 2, 3, 3, 5, 6, 5, 10, 12, 13, 7, 16, 21, 23, 24, 11, 29, 40, 45, 47, 48, 15, 45, 67, 78, 83, 85, 86, 22, 75, 117, 141, 152, 157, 159, 160, 30, 115, 193, 239, 263, 274, 279, 281, 282, 42, 181, 319, 409, 457, 481, 492, 497, 499, 500, 56, 271, 510, 674, 768, 816, 840, 851, 856, 858, 859 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Rows n = 1..200, flattened P. A. MacMahon, The connexion between the sum of the squares of the divisors and the number of partitions of a given number, Messenger Math., 54 (1924), 113-116. Collected Papers, MIT Press, 1978, Vol. I, pp. 1364-1367. See Table II. EXAMPLE Triangle begins: [1] [2, 3] [3, 5, 6] [5, 10, 12, 13] [7, 16, 21, 23, 24] [11, 29, 40, 45, 47, 48] [15, 45, 67, 78, 83, 85, 86] [22, 75, 117, 141, 152, 157, 159, 160] ... The square array (A242641 with n=0 column omitted) begins: 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, ... 1, 3, 5, 10, 16, 29, 45, 75, 115, 181, 271, 413, ... 1, 3, 6, 12, 21, 40, 67, 117, 193, 319, 510, 818, ... 1, 3, 6, 13, 23, 45, 78, 141, 239, 409, 674, 1116, ... 1, 3, 6, 13, 24, 47, 83, 152, 263, 457, 768, 1292, ... 1, 3, 6, 13, 24, 48, 85, 157, 274, 481, 816, 1388, ... 1, 3, 6, 13, 24, 48, 86, 159, 279, 492, 840, 1436, ... ... MAPLE T:= proc(s, n) option remember; `if`(n=0, 1, add(add(min(d, s)       *d, d=numtheory[divisors](j))*T(s, n-j), j=1..n)/n)     end: seq(seq(T(s, n), s=1..n), n=1..14);  # Alois P. Heinz, Oct 02 2018 MATHEMATICA T[s_, n_] := T[s, n] = If[n==0, 1, Sum[Sum[Min[d, s]*d, {d, Divisors[j]}]* T[s, n - j], {j, 1, n}]/n]; Table[Table[T[s, n], {s, 1, n}], {n, 1, 14}] // Flatten (* Jean-François Alcover, Dec 10 2019, after Alois P. Heinz *) CROSSREFS Upper triangle of array in A242641 (with the n=0 column omitted). Sequence in context: A183322 A295918 A296834 * A178041 A181805 A212010 Adjacent sequences:  A242639 A242640 A242641 * A242643 A242644 A242645 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, May 21 2014 STATUS approved

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Last modified August 17 02:36 EDT 2022. Contains 356180 sequences. (Running on oeis4.)