Original entry on oeis.org
1, 1, 3, 21, 193, 2125, 32281, 655235, 15530705, 427214889, 14127457681, 542796582295, 23400843532969, 1140401734145453, 62743287535847465, 3822548966261363595, 256275705820386124321, 18923726002188870476497
Offset: 1
-
{a(n)=local(X=x+x*O(x^n), Egf); Egf=sum(m=0, n, x^m*prod(k=1, m, cosh(k*X))); if(n<1,0,(n-1)!*polcoeff(Egf, n))}
A193467
E.g.f.: Sum_{n>=0} x^n * exp(n*(n+1)/2*x).
Original entry on oeis.org
1, 1, 4, 27, 280, 4025, 75876, 1800253, 52193408, 1807302897, 73406128420, 3446236588421, 184750419871920, 11194423784630281, 759960096829452260, 57367378069894391325, 4783586470578255085696, 438054092182322814028001, 43827052650093379145736900
Offset: 0
E.g.f.: A(x) = 1 + x + 4*x^2/2! + 27*x^3/3! + 280*x^4/4! + 4025*x^5/5! + 75876*x^6/6! + 1800253*x^7/7! +...
where
A(x) = 1 + x*exp(x) + x^2*exp(3*x) + x^3*exp(6*x) + x^4*exp(10*x) +...
By a q-series identity:
A(x) = 1 + x*exp(x)*(1-x*exp(x))/(1-x*exp(2*x)) + x^2*exp(2*x)*(1-x*exp(x))*(1-x*exp(3*x))/((1-x*exp(2*x))*(1-x*exp(4*x))) + x^3*exp(3*x)*(1-x*exp(x))*(1-x*exp(3*x))*(1-x*exp(5*x))/((1-x*exp(2*x))*(1-x*exp(4*x))*(1-x*exp(6*x))) +...
-
{a(n)=local(Egf); Egf=sum(m=0, n, x^m*exp(m*(m+1)/2*x+x*O(x^n))); n!*polcoeff(Egf, n)}
-
/* q-series identity: */
{a(n)=local(A=1+x);for(i=1, n, A=sum(m=0, n, x^m*exp(m*x+x*O(x^n))*prod(k=1, m, (1-x*exp((2*k-1)*x+x*O(x^n)))/(1-x*exp((2*k)*x+x*O(x^n)))))); n!*polcoeff(A, n)}
Showing 1-2 of 2 results.
Comments