A204855 G.f.: Sum_{n>=0} x^(n*(n+1)/2) / Product_{k=1..n} (1 - (n-k+1)*x^k).

1, 1, 1, 2, 3, 6, 12, 25, 54, 120, 278, 666, 1671, 4355, 11804, 33019, 94960, 279219, 836907, 2550991, 7901818, 24875931, 79667065, 259892494, 864832484, 2938862050, 10204420451, 36199678110, 131086662067, 483853193560, 1817012289562, 6927980565530

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..250

Example

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 6*x^5 + 12*x^6 + 25*x^7 +...
where A(x) = 1 + x/(1-x) + x^3/((1-2*x)*(1-x^2)) + x^6/((1-3*x)*(1-2*x^2)*(1-x^3)) + x^10/((1-4*x)*(1-3*x^2)*(1-2*x^3)*(1-x^4)) +...

Prog

(PARI) {a(n)=polcoeff(1+sum(m=1, n, x^(m*(m+1)/2)/prod(k=1, m, 1-(m-k+1)*x^k+x*O(x^n))), n)}

Crossrefs

Cf. A204856, A204857.

Sequence in context: A162985 A052523 A262430 * A259098 A367386 A166296

Adjacent sequences: A204852 A204853 A204854 * A204856 A204857 A204858

Keyword

nonn

Author

Paul D. Hanna, Jan 20 2012

Status

approved