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 A015744 Number of partitions of n into distinct parts, none being 2. 11
 1, 1, 0, 1, 2, 2, 2, 3, 4, 5, 6, 7, 9, 11, 13, 16, 19, 22, 27, 32, 37, 44, 52, 60, 70, 82, 95, 110, 127, 146, 169, 194, 221, 254, 291, 331, 377, 429, 487, 553, 626, 707, 800, 903, 1016, 1145, 1288, 1445, 1622, 1819, 2036, 2278, 2546, 2842, 3172, 3536, 3936, 4381 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS With offset 2 (and a(0)=a(1)=0) the number of 2's in all partitions of n into distinct parts. [Joerg Arndt, Feb 20 2014] LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Cristina Ballantine, Mircea Merca, On identities of Watson type, Ars Mathematica Contemporanea (2019) Vol. 17, 277-290. FORMULA G.f.: (1+x)*product(j>=3, 1+x^j ). - Emeric Deutsch, Apr 09 2006 a(n+2)=sum_{k=1..floor(n/2)} (-1)^(k-1)*A000009(n-2*k). - Mircea Merca, Feb 20 2014 a(n) ~ exp(Pi*sqrt(n/3)) / (8*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Oct 30 2015 EXAMPLE a(8)=4 because we have [8],[7,1],[5,3] and [4,3,1]. MAPLE g:=(1+x)*product(1+x^j, j=3..80): gser:=series(g, x=0, 70): seq(coeff(gser, x, n), n=0..57); # Emeric Deutsch, Apr 09 2006 MATHEMATICA CoefficientList[Series[Product[1+q^n, {n, 1, 60}]/(1+q^2), {q, 0, 60}], q] Table[Count[Select[IntegerPartitions[n], DeleteDuplicates[#] == # &], x_ /; ! MemberQ[x, 2]], {n, 0, 57}] (* Robert Price, May 17 2020 *) CROSSREFS Cf. A025147, A015745, A015746, A015750, A015753, A015754, A015755. Sequence in context: A029049 A094983 A238218 * A118301 A018121 A256636 Adjacent sequences:  A015741 A015742 A015743 * A015745 A015746 A015747 KEYWORD nonn AUTHOR EXTENSIONS Corrected and extended by Dean Hickerson, Oct 10, 2001 STATUS approved

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Last modified May 15 01:43 EDT 2021. Contains 343909 sequences. (Running on oeis4.)