A222080 G.f.: 1 = Sum_{n>=0} a(n) * x^n * (1 - (2*n+1)*x)^2.

1, 2, 11, 92, 1013, 13726, 219919, 4057048, 84545129, 1961698586, 50111003987, 1396488977908, 42139540225501, 1368234341961718, 47547441824994647, 1760308790559597104, 69151746439874522321, 2872358517303945656242, 125758844338252841129371, 5787515297333376814677004

Offset

0,2

Comments

A self-convolution of an integer sequence (A222081).

Links

Paul D. Hanna, Table of n, a(n) for n = 0..300

Example

The terms satisfy:
1 = (1-x)^2 + 2*x*(1-3*x)^2 + 11*x^2*(1-5*x)^2 + 92*x^3*(1-7*x)^2 + 1013*x^4*(1-9*x)^2 + 13726*x^5*(1-11*x)^2 + 219919*x^6*(1-13*x)^2 +...
G.f.: A(x) = 1 + 2*x + 11*x^2 + 92*x^3 + 1013*x^4 + 13726*x^5 + 219919*x^6 + 4057048*x^7 + 84545129*x^8 +...
The square-root of g.f. A(x) is an integer series:
A(x)^(1/2) = 1 + x + 5*x^2 + 41*x^3 + 453*x^4 + 6205*x^5 + 100649*x^6 + 1878277*x^7 + 39534033*x^8 +...+ A222081(n)*x^n +...

Prog

(PARI) {a(n)=polcoeff(1-sum(m=0, n-1, a(m)*x^m*(1-(2*m+1)*x+x*O(x^n))^2), n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A222081.

Sequence in context: A143870 A047854 A366402 * A122708 A337012 A322767

Adjacent sequences: A222077 A222078 A222079 * A222081 A222082 A222083

Keyword

nonn

Author

Paul D. Hanna, Feb 07 2013

Status

approved