OFFSET
0,5
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..300
EXAMPLE
G.f.: A(x) = 1 + x^2 + 3*x^4 + 4*x^5 + 20*x^6 + 62*x^7 + 251*x^8 + 1002*x^9 + 4295*x^10 + 19086*x^11 + 88369*x^12 + 423957*x^13 + 2104214*x^14 + ...
such that the following series are equal
B(x) = 1 + A(x)*x + A(x)^3*x^2 + A(x)^6*x^3 + A(x)^10*x^4 + A(x)^15*x^5 + A(x)^21*x^6 + A(x)^28*x^7 + A(x)^36*x^8 + A(x)^45*x^9 + ...
and
B(x) = 1 + x + (1+x)*x^2 + (1+x)^3*x^3 + (1+x)^6*x^4 + (1+x)^10*x^5 + (1+x)^15*x^6 + (1+x)^21*x^7 + (1+x)^28*x^8 + (1+x)^36*x^9 + ...
where
B(x) = 1 + x + x^2 + 2*x^3 + 4*x^4 + 10*x^5 + 27*x^6 + 81*x^7 + 262*x^8 + 910*x^9 + 3363*x^10 + 13150*x^11 + 54135*x^12 + ... + A121690(n-1)*x^n + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A[#A]=polcoeff( sum(m=0, #A, x^m*(1+x +x*O(x^#A))^(m*(m-1)/2) - x^m*Ser(A)^(m*(m+1)/2) ), #A)); A[n+1]}
for(n=0, 35, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 03 2019
STATUS
approved