A278298 Expansion of ((sqrt(2);x)_inf + (-sqrt(2);x)_inf - 2)/4, where(a;q)_inf is the q-Pochhammer symbol.

1, 1, 2, 2, 3, 5, 6, 8, 11, 15, 18, 24, 29, 37, 48, 58, 71, 89, 108, 132, 163, 195, 236, 284, 341, 405, 486, 578, 683, 809, 954, 1120, 1319, 1543, 1806, 2112, 2457, 2857, 3320, 3850, 4451, 5149, 5936, 6840, 7879, 9047, 10376, 11900, 13613, 15561, 17770, 20266

Offset

1,3

Comments

The q-Pochhammer symbol (a;q)_inf = Product_{k>=0} (1 - a*q^k).

a(n) agrees with A118399(n) for n < 15.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Eric Weisstein's World of Mathematics, q-Pochhammer Symbol.

Formula

a(n) ~ sqrt(1 + sqrt(2)) * c^(1/4) * exp(2*sqrt(c*n)) / (8*sqrt(Pi)*n^(3/4)), where c = Pi^2/6 + log(2)^2/8 + polylog(2, -1/sqrt(2)) = 1.0944511783086747574574059... - Vaclav Kotesovec, Oct 11 2018

Mathematica

((QPochhammer[Sqrt[2], x] + QPochhammer[-Sqrt[2], x] - 2)/4 + O[x]^53)[[3]]

Crossrefs

Cf. A118399, A278296.

Sequence in context: A121081 A330952 A118399 * A178927 A076571 A084783

Adjacent sequences: A278295 A278296 A278297 * A278299 A278300 A278301

Keyword

nonn

Author

Vladimir Reshetnikov, Nov 17 2016

Status

approved