The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A278297 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A278297

a(n) = A278296(n) - A238132(n).
(history; published version)

#8 by Peter Luschny at Sat Nov 19 02:58:41 EST 2016

STATUS

reviewed

approved

#7 by G. C. Greubel at Fri Nov 18 23:59:44 EST 2016

STATUS

proposed

reviewed

#6 by Vladimir Reshetnikov at Fri Nov 18 17:49:20 EST 2016

STATUS

editing

proposed

#5 by Vladimir Reshetnikov at Fri Nov 18 17:49:13 EST 2016

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/q-PolygammaFunction.html">q-Polygamma Function</a>, <a href="http://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>.

FORMULA

G.f.: Sum_{k>=0} (2^n - 2*n) * x^(n*(2*n+1)) / (x; x)_{2*n}, where (a; q)_n = Product_{k=0..n-1} (1 - a*q^n) is the q-Pochhammer symbol.

G.f.: ((sqrt(2)-1)*(-sqrt(2); x)_inf - (sqrt(2)+1)*(sqrt(2); x)_inf)/2 + (2*(x; x)_inf * (log(1-x) + psi_x(1)) + (-1; x)_inf * (log(1-x) + psi_x(1 - log(-1)/log(x))))/(4*log(x)), where psi_q(z) is the q-digamma function, and (a; q)_inf = Product_{k>=0} (1 - a*q^n) is the q-Pochhammer symbol (the Euler function), log(-1) = i*Pi.

MATHEMATICA

Table[SeriesCoefficient[FunctionExpand[Sum[(2^n - 2 n) x^(n (2 n + 1))/QPochhammer[x, x, 2 n], {n, 0, Sqrt[k/2]}]], {x, 0, k}], {k, 0, 60}]

STATUS

approved

editing

#4 by Peter Luschny at Fri Nov 18 00:30:38 EST 2016

STATUS

proposed

approved

#3 by Vladimir Reshetnikov at Thu Nov 17 00:22:09 EST 2016

STATUS

editing

proposed

Discussion

Thu Nov 17

08:37

Peter Luschny: Vladimir, please see my comment in A032302.

#2 by Vladimir Reshetnikov at Thu Nov 17 00:21:16 EST 2016

NAME

allocated for Vladimir Reshetnikov

a(n) = A278296(n) - A238132(n).

DATA

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 6, 10, 14, 22, 28, 40, 52, 70, 88, 116, 142, 180, 228, 280, 342, 422, 510, 620, 750, 902, 1084, 1296, 1544, 1834, 2182, 2574, 3042, 3580, 4208, 4920, 5762, 6728, 7838, 9108, 10574, 12240

OFFSET

0,22

CROSSREFS

Cf. A278296, A238132.

KEYWORD

allocated

nonn

AUTHOR

Vladimir Reshetnikov, Nov 17 2016

STATUS

approved

editing

#1 by Vladimir Reshetnikov at Thu Nov 17 00:21:16 EST 2016

NAME

allocated for Vladimir Reshetnikov

KEYWORD

allocated

STATUS

approved