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URL: https://oeis.org/A278402

⇱ A278402 - OEIS

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A278402
G.f.: Im(2/(i; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).
5
1, 1, 0, -1, -1, -1, -3, -3, -2, -2, -2, -2, -1, 1, 1, 2, 5, 7, 7, 8, 11, 12, 12, 13, 15, 16, 14, 12, 12, 11, 6, 2, 1, -3, -10, -17, -21, -27, -37, -45, -50, -57, -68, -77, -81, -86, -96, -102, -101, -103, -108, -109, -103, -97, -95, -88, -71, -54, -42, -24, 5
OFFSET
0,7
COMMENTS
The q-Pochhammer symbol (a; q)_inf = Product_{k>=0} (1 - a*q^k).
LINKS
Eric Weisstein's World of Mathematics, q-Pochhammer Symbol.
FORMULA
2/(i; x)_inf is the g.f. for A278401(n) + i*a(n).
G.f.: Sum_{n >= 0} (-1)^n*x^(2*n)*(1 + x - x^(2*n+1))/Product_{k = 1..2*n+1} (1 - x^k). - Peter Bala, Feb 09 2021
MAPLE
with(gfun): series( add( (-1)^n*x^(2*n)*(1 + x - x^(2*n+1))/mul(1 - x^k, k = 1..2*n+1), n = 0..50), x, 101): seriestolist(%); # Peter Bala, Feb 09 2021
MATHEMATICA
Im[(2/QPochhammer[I, x] + O[x]^70)[[3]]]
CROSSREFS
KEYWORD
sign
AUTHOR
STATUS
approved