A206119 G.f.: A(x) = Sum_{n>=0} x^n / Product_{k=1..n} (1-x^k)^(n-k+1).

1, 1, 2, 4, 9, 20, 46, 106, 247, 578, 1359, 3204, 7573, 17930, 42512, 100902, 239694, 569768, 1355083, 3224124, 7673612, 18268414, 43500301, 103599089, 246761629, 587822094, 1400398656, 3336473471, 7949650646, 18942098721, 45136103113, 107555568419, 256302098369

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Formula

a(n) ~ c / r^n, where r = A347968 = 0.419600352598356478498775753566700025318089363120016078... is the root of the equation QPochhammer(r) = r and c = 0.21842597743526022597060618810878279... - Vaclav Kotesovec, Aug 21 2018

Example

G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 20*x^5 + 46*x^6 + 106*x^7 +...
where
A(x) = 1 + x/(1-x) + x^2/((1-x)^2*(1-x^2)) + x^3/((1-x)^3*(1-x^2)^2*(1-x^3)) + x^4/((1-x)^4*(1-x^2)^3*(1-x^3)^2*(1-x^4)) +...

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n, x^m/prod(k=1, m, (1-x^k +x*O(x^n))^(m-k+1))), n)}

Crossrefs

Cf. A067687.

Sequence in context: A191827 A000968 A005908 * A085748 A317097 A252354

Adjacent sequences: A206116 A206117 A206118 * A206120 A206121 A206122

Keyword

nonn

Author

Paul D. Hanna, Feb 03 2012

Status

approved