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 A116688 Sum over all partitions of n of the sum of the parts that are smaller than the largest part. 1
 0, 0, 1, 3, 9, 17, 36, 61, 106, 171, 273, 411, 627, 916, 1326, 1890, 2667, 3698, 5102, 6943, 9388, 12588, 16747, 22113, 29051, 37914, 49191, 63515, 81589, 104315, 132799, 168351, 212540, 267395, 335085, 418574, 521093, 646763, 800164, 987315 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n)=Sum(k*A116687(n,k),k>=0). LINKS Table of n, a(n) for n=1..40. FORMULA G.f.=sum(x^i*sum(jx^j/(1-x^j), j=1..i-1)/product(1-x^q, q=1..i), i=1..infinity). a(n) = n*A000041(n) - A092321(n). - Vladeta Jovovic, Feb 24 2006 EXAMPLE a(5)=9 because the partitions of 5 are [5],[4,(1)],[3,(2)],[3,(1),(1)], [2,2,(1)],[2,(1),(1),(1)] and [1,1,1,1,1] and the sum of the parts (shown between parentheses) that are smaller than the largest part is 1+2+1+1+1+1+1+1=9. MAPLE f:=sum(x^i*sum(j*x^j/(1-x^j), j=1..i-1)/product(1-x^q, q=1..i), i=1..55): fser:=series(f, x=0, 50): seq(coeff(fser, x^n), n=1..47); CROSSREFS Cf. A116687. Sequence in context: A294425 A123325 A239206 * A293423 A011755 A262466 Adjacent sequences: A116685 A116686 A116687 * A116689 A116690 A116691 KEYWORD nonn AUTHOR Emeric Deutsch, Feb 23 2006 STATUS approved

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Last modified August 8 12:42 EDT 2024. Contains 375021 sequences. (Running on oeis4.)