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A278297 a(n) = A278296(n) - A238132(n). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,22
LINKS
Eric Weisstein's World of Mathematics, q-Polygamma Function, q-Pochhammer Symbol.
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}]
CROSSREFS
Sequence in context: A240310 A083848 A330644 * A139582 A300415 A355908
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)