A106223 Self-convolution 5th power equals A106222, which consists entirely of digits {0,1,2,3,4} after the initial terms {1,5}.

1, 1, -2, 6, -21, 80, -320, 1326, -5637, 24434, -107541, 479192, -2157027, 9792618, -44780207, 206053429, -953296364, 4431418833, -20686477329, 96930426941, -455717114981, 2149060994827, -10162417338993, 48176297258115, -228910042632050, 1089957826522693, -5199911987465160

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

Limit a(n+1)/a(n) = -5.001596426773442826534115368782519...

Example

A(x) = 1 + x - 2*x^2 + 6*x^3 - 21*x^4 + 80*x^5 - 320*x^6 +-...
A(x)^5 = 1 + 5*x + x^5 + 3*x^10 + x^15 + 4*x^20 + x^35 +...
A106222 = {1,5,0,0,0,1,0,0,0,0,3,0,0,0,0,1,0,0,0,0,4,...}.

Prog

(PARI) {a(n)=local(A=1+5*x); if(n==0, 1, for(j=1, n, for(k=0, 4, t=polcoeff((A+k*x^j+x*O(x^j))^(1/5), j); if(denominator(t)==1, A=A+k*x^j; break))); return(polcoeff((A+x*O(x^n))^(1/5), n)))}

Crossrefs

Cf. A106222, A106219, A106221, A106225.

Sequence in context: A150200 A150201 A150202 * A196345 A352703 A352704

Adjacent sequences: A106220 A106221 A106222 * A106224 A106225 A106226

Keyword

sign,base

Author

Paul D. Hanna, May 01 2005

Status

approved