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A173613
Even bisection of A173610.
3
1, 2, 10, 60, 384, 2752, 19436, 132888, 938448, 6977712, 52748180, 402295360, 3045774336, 22798000896, 169191995264, 1244649595008, 9253079696256, 69936818500032, 532964898123840, 4089541311972480, 31558707924799104
OFFSET
0,2
FORMULA
a(n) = A173611(n)*A173611(n-1) for n>0, with a(0)=1, where A173611 is the self-convolution of A173610.
EXAMPLE
G.f.: A(x) = 1 + 2*x + 10*x^2 + 60*x^3 + 384*x^4 + 2752*x^5 +...
Describe the g.f. of A173610 by:
B(x) = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 25*x^5 + 60*x^6 + 144*x^7 +...
then the g.f. of A173611 is given by C(x) = B(x)^2:
C(x) = 1 + 2*x + 5*x^2 + 12*x^3 + 32*x^4 + 86*x^5 +...
where the product of adjacent coefficients of C(x) form this sequence
and yields the even bisection of A173610.
PROG
(PARI) {a(n)=local(A=1+x, B); for(i=1, n, B=(A+x*O(x^n))^2; A=1+x*sum(m=0, n\2, polcoeff(B, m)*polcoeff(B, m+1)*x^(2*m+1)) +x*sum(m=0, n\2, polcoeff(B, m)^2*x^(2*m))); if(n==0, 1, polcoeff(A^2, n)*polcoeff(A^2, n-1))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 22 2010
STATUS
approved