The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A292042

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A292042

G.f.: Re((i*x; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).
(history; published version)

#37 by N. J. A. Sloane at Tue Jan 19 21:53:28 EST 2021

STATUS

proposed

approved

#36 by Jon E. Schoenfield at Tue Jan 19 19:53:31 EST 2021

STATUS

editing

proposed

#35 by Jon E. Schoenfield at Tue Jan 19 19:53:26 EST 2021

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proposed

editing

#34 by Jon E. Schoenfield at Tue Jan 19 19:50:59 EST 2021

STATUS

editing

proposed

Discussion

Tue Jan 19

19:53

Jon E. Schoenfield: (Well, the change about the parentheses is for consistency with other entries in the OEIS that are consistent with the Style Sheet.)  :-)

#33 by Jon E. Schoenfield at Tue Jan 19 19:50:31 EST 2021

FORMULA

G.f.: A(x) = Sum_{n >= 0} (-1)^n*x^(n*(2*n+1))/(Product_{k = 1..2*n} (1 - x^k). Cf. A035294.

Conjectural g.f.: A(x) = (1/2)*Sum_{n >= 0} (-x)^(n*(n-1)/2)/(Product_{k = 1..n} (1 - x^k). (End)

STATUS

proposed

editing

Discussion

Tue Jan 19

19:50

Jon E. Schoenfield: (Product format corrected per the Style Sheet.)

#32 by Peter Bala at Tue Jan 19 16:19:51 EST 2021

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editing

proposed

#31 by Peter Bala at Tue Jan 19 16:19:46 EST 2021

MAPLE

S := convert(series( (1/2)*add( (-1)^n*x)^(n*(2*n-+1)/2)/(mul(1 - x^k, k = 1..2*n)), n = 0..1+floor(sqrt(2*N/2)) ), x, N+1 ), polynom):

#30 by Peter Bala at Mon Jan 18 11:33:59 EST 2021

FORMULA

From Peter Bala, Jan 15 2021: (Start)

G.f.: A(1/2x)* = Sum_{n >= 0} (-1)^n*x)^(n*(2*n-+1)/2)/(Product_{k = 1..2*n} 1 - x^k). Cf. A035294. - _Peter Bala_, Jan 15 2021

Conjectural g.f.: A(x) = (1/2)*Sum_{n >= 0} (-x)^(n*(n-1)/2)/(Product_{k = 1..n} 1 - x^k). (End)

CROSSREFS

Cf. A035294, A278399, A278400, A278420, A292043, A292052.

#29 by Peter Bala at Fri Jan 15 12:03:07 EST 2021

FORMULA

G.f.: (1/2)*Sum_{n >= 0} (-x)^(n*(n-1)/2)/Product_{k = 1..n} 1 - x^k. - Peter Bala, Jan 15 2021

MAPLE

N:= 100:

S := convert(series( (1/2)*add( (-x)^(n*(n-1)/2)/(mul(1 - x^k, k = 1..n)), n = 0..1+floor(sqrt(2*N)) ), x, N+1 ), polynom):

seq(coeff(S, x, n), n = 0..N); # Peter Bala, Jan 15 2021

STATUS

approved

editing

#28 by Joerg Arndt at Sat Sep 09 06:12:32 EDT 2017

STATUS

proposed

approved