A202947 G.f.: [ Sum_{n>=0} (n+1) * 2^(n^2) * x^n ]^(1/2).

1, 2, 22, 980, 161638, 100318460, 240313495420, 2251316821283048, 83005840299778004614, 12089092134684999622076396, 6972054121242613685463168904468, 15950722005044706228925521886595357720, 144954811888851643278920459489891540357638876

Offset

0,2

Comments

Equals the self-convolution square-root of A197927 (with offset).

Links

Table of n, a(n) for n=0..12.

Formula

a(n) = (n+1)*2^(n^2-1) - Sum_{k=1..n-1} a(n-k)*a(k)/2 for n>0 with a(0)=1.

Example

G.f.: A(x) = 1 + 2*x + 22*x^2 + 980*x^3 + 161638*x^4 + 100318460*x^5 +...
where
A(x)^2 = 1 + 2*2*x + 3*2^4*x^2 + 4*2^9*x^3 + 5*2^16*x^4 + 6*2^25*x^5 +...
more explicitly,
A(x)^2 = 1 + 4*x + 48*x^2 + 2048*x^3 + 327680*x^4 + 201326592*x^5 +...+ A197927(n+1)*x^n +...

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n, (m+1)*2^(m^2)*x^m+x*O(x^n))^(1/2), n)}
(PARI) {a(n)=if(n==0, 1, (n+1)*2^(n^2-1)-sum(k=1, n-1, a(n-k)*a(k)/2))}

Crossrefs

Cf. A197927, A202942.

Sequence in context: A279802 A015210 A152558 * A177410 A193486 A337577

Adjacent sequences: A202944 A202945 A202946 * A202948 A202949 A202950

Keyword

nonn

Author

Paul D. Hanna, Dec 26 2011

Status

approved