A222081 Self-convolution equals A222080.

1, 1, 5, 41, 453, 6205, 100649, 1878277, 39534033, 924986401, 23790991061, 666732284009, 20211529694661, 658743175016461, 22964324182662569, 852450674859207605, 33563386167190876321, 1396839898167086931137, 61260669590285253202981, 2823455397312949805962921

Offset

0,3

Comments

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

Links

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

Formula

a(n) == 1 (mod 4).

Limit A222080(n)/a(n) = 2.

Example

G.f.: A(x) = 1 + x + 5*x^2 + 41*x^3 + 453*x^4 + 6205*x^5 + 100649*x^6 +...
where
A(x)^2 = 1 + 2*x + 11*x^2 + 92*x^3 + 1013*x^4 + 13726*x^5 + 219919*x^6 +...+ A222080(n)*x^n +...
such that A222080 satisfies:
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 +...+ A222080(n)*x^n*(1 - (2*n+1)*x)^2 +...

Prog

(PARI) {A222080(n)=polcoeff(1-sum(m=0, n-1, A222080(m)*x^m*(1-(2*m+1)*x+x*O(x^n))^2), n)}
{a(n)=polcoeff(sqrt(sum(k=0, n, A222080(k)*x^k+x*O(x^n))), n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A222080.

Sequence in context: A115257 A225095 A302100 * A047735 A096364 A210661

Adjacent sequences: A222078 A222079 A222080 * A222082 A222083 A222084

Keyword

nonn

Author

Paul D. Hanna, Feb 07 2013

Status

approved