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 A130780 Number of partitions of n such that number of odd parts is greater than or equal to number of even parts. 15
 1, 1, 1, 3, 3, 6, 8, 12, 16, 23, 32, 42, 58, 75, 102, 131, 173, 220, 288, 363, 466, 587, 743, 929, 1164, 1448, 1797, 2224, 2738, 3368, 4122, 5042, 6133, 7466, 9035, 10941, 13184, 15888, 19064, 22876, 27343 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n) = A108950(n) + A045931(n) = A000041(n) - A108949(n). - Reinhard Zumkeller, Jan 21 2010 a(n) = Sum_{k=0..n} A240009(n,k). - Alois P. Heinz, Mar 30 2014 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 FORMULA G.f.: Sum_{k>=0} x^k/Product_{i=1..k} (1-x^(2*i))^2. EXAMPLE a(5)=6 because we have 5,41,32,311,211 and 11111 (221 does not qualify). MAPLE g:=sum(x^k/(product((1-x^(2*i))^2, i=1..k)), k=0..50): gser:=series(g, x=0, 50): seq(coeff(gser, x, n), n=1..40); # Emeric Deutsch, Aug 24 2007 # second Maple program: b:= proc(n, i, t) option remember; `if`(n=0,       `if`(t>=0, 1, 0), `if`(i<1, 0, b(n, i-1, t)+       `if`(i>n, 0, b(n-i, i, t+(2*irem(i, 2)-1)))))     end: a:= n-> b(n\$2, 0): seq(a(n), n=0..80);  # Alois P. Heinz, Mar 30 2014 MATHEMATICA \$RecursionLimit = 1000; b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t >= 0, 1, 0],  If[i<1, 0, b[n, i-1, t] + If[i>n, 0, b[n-i, i, t + (2*Mod[i, 2]-1)]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 80}] (* Jean-François Alcover, May 12 2015, after Alois P. Heinz *) CROSSREFS Cf. A045931, A108949, A108950. Cf. A171966, A171967. - Reinhard Zumkeller, Jan 21 2010 Sequence in context: A241390 A241831 A239946 * A174524 A143592 A280197 Adjacent sequences:  A130777 A130778 A130779 * A130781 A130782 A130783 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Aug 19 2007 EXTENSIONS More terms from Emeric Deutsch, Aug 24 2007 STATUS approved

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Last modified October 21 04:26 EDT 2019. Contains 328291 sequences. (Running on oeis4.)