A352094 Column 2 of triangle A352093.

1, 8, 46, 256, 1286, 6400, 30348, 142352, 652486, 2958864, 13238308, 58745872, 258345884, 1128790784, 4900778456, 21168054432, 90993848134, 389548241904, 1661387607860, 7062104700176, 29927650910900, 126478906062144, 533174476617768, 2242449423806688

Offset

1,2

Comments

This sequence gives the coefficients of x^n*y^2 in the g.f. of triangle A352093, for n >= 1; the g.f. of triangle A352093 equals lim_{N->infinity} (1 - P(N,x,y))/(2*x)^N, where P(0,x,y) = -y, and P(n+1,x,y) = sqrt(1 - 4*x + 4*x*P(n,x,y)) for n = 0..N-1.

The two preceding columns of triangle A352093 are A351509 and A351511.

Links

Table of n, a(n) for n=1..24.

Formula

Sum_{n>=1} a(n)/8^n = 1/2.

Example

G.f. A(x) = x + 8*x^2 + 46*x^3 + 256*x^4 + 1286*x^5 + 6400*x^6 + 30348*x^7 + 142352*x^8 + 652486*x^9 + 2958864*x^10 + ...
Specific values.
A(1/8) = 1/2 = 1/8 + 8/8^2 + 46/8^3 + 256/8^4 + 1286/8^5 + 6400/8^6 + ...

Prog

(PARI) {a(n) = my(A, P = -y + x*O(x^(2*n+1)));
for(i=1, n+1, P = sqrt(1 - 4*x + 4*x*P +x*O(x^(2*n+1))); );
A = subst(derivn( (1 - P)/(2*x)^(n+1) , 2, y)/2, y, 0); polcoeff(A, n, x)}
for(n=1, 25, print1(a(n), ", "))

Crossrefs

Cf. A352093, A351509, A351511.

Sequence in context: A052244 A083421 A113992 * A037070 A141788 A317224

Adjacent sequences: A352091 A352092 A352093 * A352095 A352096 A352097

Keyword

nonn

Author

Paul D. Hanna, Mar 05 2022

Status

approved