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A118195 Self-convolution square-root of A118191, where A118191 is column 0 of the matrix square of triangle A118190 with A118190(n,k) = (5^k)^(n-k). 1
1, 1, 3, 23, 411, 15771, 1353045, 252512065, 106798723795, 99080638950595, 208993838938550873, 968425792397232696773, 10208662119796586878979989, 236472963735267887311598074949, 12462692176683507314938059670486683 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

In general, sqrt( Sum_{n>=0} x^n/(1 - q^n*x) ) is an integer series whenever q == 1 (mod 4).

LINKS

Table of n, a(n) for n=0..14.

FORMULA

G.f.: A(x) = sqrt( Sum_{n>=0} x^n/(1-5^n*x) ).

EXAMPLE

A(x) = 1 + x + 3*x^2 + 23*x^3 + 411*x^4 + 15771*x^5 +...

A(x)^2 = 1 + 2*x + 7*x^2 + 52*x^3 + 877*x^4 + 32502*x^5 +...

= 1/(1-x) + x/(1-5x) + x^2/(1-25x) + x^3/(1-125x) +...

PROG

(PARI) a(n)=polcoeff(sqrt(sum(k=0, n, sum(j=0, k, (5^j)^(k-j) )*x^k+x*O(x^n))), n)

CROSSREFS

Cf. A118190.

Sequence in context: A178315 A210910 A280654 * A055326 A271851 A133338

Adjacent sequences:  A118192 A118193 A118194 * A118196 A118197 A118198

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Apr 15 2006

STATUS

approved

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Last modified September 23 12:53 EDT 2020. Contains 337310 sequences. (Running on oeis4.)