The On-Line Encyclopedia of Integer Sequences (OEIS)

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A217569

Expansion of H(q)*G(q^11) where H and G are respectively the g.f. of A003106 and A003114 (Rogers-Ramanujan functions).
(history; published version)

#25 by Peter Luschny at Sun Nov 12 03:58:18 EST 2017

STATUS

reviewed

approved

#24 by Joerg Arndt at Sun Nov 12 02:56:54 EST 2017

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proposed

reviewed

#23 by Michel Marcus at Sat Nov 11 23:22:44 EST 2017

STATUS

editing

proposed

#22 by Michel Marcus at Sat Nov 11 23:22:39 EST 2017

FORMULA

G.f. : H(q)*G(q^11) where G(q) = Sum_{n>=0} q^(n^2)/Product_{k=1..n} (1-q^k) and H(q) = Sum_{n>=0} q^(n^2+n)/Product_{k=1..n} (1-q^k).

STATUS

proposed

editing

#21 by Jon E. Schoenfield at Sat Nov 11 17:09:31 EST 2017

STATUS

editing

proposed

#20 by Jon E. Schoenfield at Sat Nov 11 17:09:28 EST 2017

COMMENTS

With E(q) = prod(Product_{n>=1, } (1-q^n) we have G(q)*H(q) - E(q^5)/E(q), G(q) = ( E(q^8)/E(q^2) * (G(q^16) + q*H(-q^4)) ), and H(q) = ( E(q^8)/E(q^2) * (q^3*H(q^16) + G(-q^4)) ), see the Berkovich/Yesilyurt reference.

FORMULA

G.f. H(q)*G(q^11) where G(q) = sum(Sum_{n>=0, } q^(n^2)/prod(Product_{k=1..n, } (1-q^k) ) and H(q) = sum(Sum_{n>=0, } q^(n^2+n)/prod(Product_{k=1..n, } (1-q^k) ).

G.f.: 1 / prod(Product_{k>=0, } (1 - q^k ) where k (mod 55) is restricted to the set {2, 3, 7, 8, 11, 12, 13, 17, 18, 22, 23, 27, 28, 32, 33, 37, 38, 42, 43, 44, 47, 48, 52, 53} (the set has 24 elements).

STATUS

approved

editing

#19 by T. D. Noe at Sat Dec 29 15:21:35 EST 2012

STATUS

proposed

approved

#18 by Michel Marcus at Sat Dec 29 14:22:02 EST 2012

STATUS

editing

proposed

#17 by Michel Marcus at Sat Dec 29 13:40:12 EST 2012

NAME

Expansion of H(q)*G(q^11) where H and G are respectively the the g.f. of A003106 and A003114 (Rogers-Ramanujan functions).

STATUS

approved

editing

#16 by Joerg Arndt at Sun Oct 07 07:49:05 EDT 2012

STATUS

editing

approved