A293601 Limit of rows in rectangular array A292929.

2, -4, 8, -12, 24, -32, 64, -68, 152, -120, 392, -124, 1000, 320, 3056, 2836, 10280, 15112, 38668, 68348, 154152, 297948, 633352, 1269884, 2649892, 5395272, 11157512, 22890976, 47251564, 97224304, 200605456, 413622556, 853809232, 1762332664, 3640315888, 7521114700, 15545862696, 32142131064, 66481012488, 137544496052

Offset

0,1

Comments

The g.f. of A292929 is R(x,q) = sqrt( Q(x,q) / Q(x,-q) ), where Q(x,q) = Sum_{n=-oo..+oo} (x - q^n)^n; the g.f. of this sequence equals the limit of the coefficient of x^n in R(x,q) / q^n as a power series in q.

a(n+1)/a(n) tends to 2.0946... - Vaclav Kotesovec, Oct 23 2017

Links

Paul D. Hanna, Table of n, a(n) for n = 0..200

Formula

G.f.: A(q) = 2 - 4*q + 8*q^2 - 12*q^3 + 24*q^4 - 32*q^5 + 64*q^6 - 68*q^7 + 152*q^8 - 120*q^9 + 392*q^10 - 124*q^11 + 1000*q^12 + 320*q^13 + 3056*q^14 + 2836*q^15 + 10280*q^16 + 15112*q^17 + 38668*q^18 +...

Let R(x,q) be the g.f. of A292929, then we can illustrate the g.f. of this sequence as follows.

The coefficient of x^4 in R(x,q) begins:

2*q^4 - 4*q^5 + 8*q^6 - 12*q^7 + 24*q^8 - 40*q^9 + 38*q^10 +...

The coefficient of x^5 in R(x,q) begins:

2*q^5 - 4*q^6 + 8*q^7 - 12*q^8 + 24*q^9 - 32*q^10 + 48*q^11 +...

The coefficient of x^6 in R(x,q) begins:

2*q^6 - 4*q^7 + 8*q^8 - 12*q^9 + 24*q^10 - 32*q^11 + 64*q^12 +...

The g.f. A(q) equals the limit of the coefficient if x^n in R(x,q)/q^n.

Crossrefs

Cf. A292929.

Sequence in context: A032473 A084422 A175841 * A171647 A089821 A343419

Adjacent sequences: A293598 A293599 A293600 * A293602 A293603 A293604

Keyword

sign

Author

Paul D. Hanna, Oct 22 2017

Status

approved