The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A265245 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A265245

Triangle read by rows: T(n,k) is the number of partitions of n for which the sum of the squares of the parts is k (n>=0, k>=0).
(history; published version)

#14 by Susanna Cuyler at Tue Feb 19 09:21:18 EST 2019

STATUS

proposed

approved

#13 by Jean-François Alcover at Tue Feb 19 02:49:35 EST 2019

STATUS

editing

proposed

#12 by Jean-François Alcover at Tue Feb 19 02:49:30 EST 2019

MATHEMATICA

m = 8; CoefficientList[#, t]& /@ CoefficientList[1/Product[(1 - t^(k^2)* x^k), {k, 1, m}] + O[x]^m, x] // Flatten (* Jean-François Alcover, Feb 19 2019 *)

STATUS

approved

editing

#11 by R. J. Mathar at Mon Dec 14 03:51:28 EST 2015

STATUS

editing

approved

#10 by R. J. Mathar at Mon Dec 14 03:51:18 EST 2015

CROSSREFS

Cf. A000041, A066183, A229325, A229326, A229327, A229328, A229329, A229330, A229331, - A229332, A265246, A264402, A265247, A265248, A265249, A265250, A262251, A265252, - A265253.

STATUS

approved

editing

#9 by Alois P. Heinz at Sun Dec 06 10:48:33 EST 2015

STATUS

editing

approved

#8 by Alois P. Heinz at Sun Dec 06 10:47:42 EST 2015

FORMULA

G.f.: G(t,x) = 1/Product_{k >=1} (1 - t^{k^2}*x^k).

CROSSREFS

Cf. A000041, A066183, A229325, A229326, A229327, A229328, A229329, A229330, A229331, A229332, A265246, A265247, A265248, A265249, A265250, A262251, A265252, A265253.

STATUS

reviewed

editing

#7 by Emeric Deutsch at Sun Dec 06 10:37:32 EST 2015

STATUS

proposed

reviewed

#6 by Michel Marcus at Sun Dec 06 10:34:54 EST 2015

STATUS

editing

proposed

Discussion

Sun Dec 06

10:37

Emeric Deutsch: Thanks.

#5 by Michel Marcus at Sun Dec 06 10:34:44 EST 2015

LINKS

Guo-Niu Han, <a href="http://arxiv.org/abs/0804.1849">An explicit expansion formula for the powers of the Euler Product in terms of partition hook lengths</a>, arXiv:0804.1849 [math.CO], 2008.

FORMULA

G.f.: G(t,x) = 1/Product_{k >=1..infinity}(1 - t^{k^2}*x^k).

STATUS

proposed

editing