A228193 - OEIS

%I #6 Aug 20 2024 15:31:56

%S 1,3,165,488007,63015285321,313849204040245803,

%T 57549960579131376060801997,379048169979935686476204047966170767,

%U 88353684521579654155696728418892273040483607185,721871639878336367921338532273490438662977816273231098545619

%N G.f.: exp( Sum_{n>=1} A001850(n^2)*x^n/n ), where A001850 forms the central Delannoy numbers.

%F Logarithmic derivative yields A228192.

%e G.f.: A(x) = 1 + 3*x + 165*x^2 + 488007*x^3 + 63015285321*x^4 +...

%e where the logarithm of the g.f. begins:

%e log(A(x)) = 3*x + 321*x^2/2 + 1462563*x^3/3 + 252055236609*x^4/4 +...+ A001850(n^2)*x^n/n +...

%o (PARI) {A228192(n)=sum(k=0,n^2,binomial(n^2,k)*binomial(n^2+k,k))}

%o {a(n)=polcoeff(exp(sum(k=1,n+1,A228192(k)*x^k/k) +x*O(x^n)),n)}

%o for(n=0,20,print1(a(n),", "))

%Y  Cf. A228192, A001850.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Aug 15 2013