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A036469
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Partial sums of A000009 (partitions into distinct parts).
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10
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1, 2, 3, 5, 7, 10, 14, 19, 25, 33, 43, 55, 70, 88, 110, 137, 169, 207, 253, 307, 371, 447, 536, 640, 762, 904, 1069, 1261, 1483, 1739, 2035, 2375, 2765, 3213, 3725, 4310, 4978, 5738, 6602, 7584, 8697, 9957, 11383, 12993, 14809, 16857, 19161
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also number of 1's in all partitions of n+1 into odd parts. Example: a(4)=7 because the partitions of 5 into odd parts are [5], [3,1,1], [1,1,1,1,1], having a total number of 7 1's. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 29 2006
Convolved with A035363 = A000070 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 09 2009]
Equals row sums of triangle A166240. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 09 2009]
The subsequence of prime partial sums of A000009 (partitions into distinct parts) begins: 2, 3, 5, 7, 19, 43, 137, 307, 1069, 1483, 11383. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 11 2010]
a(n) = if n <= 1 then A201377(1,n) else A201377(n,1). [Reinhard Zumkeller, Dec 02 2011]
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 774
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FORMULA
| G.f.=1/[(1-x)product(1-x^(2j-1), j=1..infinity)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 29 2006
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MAPLE
| g:=1/(1-x)/product(1-x^(2*j-1), j=1..30): gser:=series(g, x=0, 50): seq(coeff(gser, x, n), n=0..46); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 29 2006
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MATHEMATICA
| CoefficientList[ Series[Product[(1 + t^i), {i, 1, Infinity}]/(1 - t), {t, 0, 46}], t] [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), May 16 2010]
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CROSSREFS
| Cf. A000009.
Cf. A035363, A000070. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 09 2009]
Cf. A166240. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 09 2009]
Sequence in context: A088585 A175842 A008581 * A116480 A023026 A096778
Adjacent sequences: A036466 A036467 A036468 * A036470 A036471 A036472
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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