A221547 G.f.: Sum_{n>=0} x^n * (1+x)^(n*(n+1)/2) / Product_{k=1..n} (1 + x*(1+x)^k).

1, 1, 1, 1, 2, 3, 7, 15, 38, 102, 291, 894, 2881, 9814, 35049, 130827, 509444, 2062695, 8667549, 37723094, 169735610, 788356105, 3774150884, 18599067832, 94236062123, 490360221092, 2617839307733, 14324884376705, 80274898974872, 460315751077622, 2698920189467845

Offset

0,5

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..210

Example

G.f.: A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 7*x^6 + 15*x^7 + 38*x^8 +...
where
A(x) = 1 + x*(1+x)/(1 + x*(1+x)) + x^2*(1+x)^3/((1+x*(1+x))*(1+x*(1+x)^2)) + x^3*(1+x)^6/((1+x*(1+x))*(1+x*(1+x)^2)*(1+x*(1+x)^3)) + x^4*(1+x)^10/((1+x*(1+x))*(1+x*(1+x)^2)*(1+x*(1+x)^3)*(1+x*(1+x)^4)) +...

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n, x^m*(1+x)^(m*(m+1)/2)/prod(k=1, m, (1+x*(1+x)^k+x*O(x^n)))), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A221546, A207081.

Sequence in context: A114584 A328779 A039826 * A289471 A289470 A161746

Adjacent sequences: A221544 A221545 A221546 * A221548 A221549 A221550

Keyword

nonn

Author

Paul D. Hanna, Jan 19 2013

Status

approved