A248655 E.g.f.: Sum_{n>=0} x^n * (2*exp(n*x) - 1)^n.

1, 1, 6, 60, 1040, 24650, 796332, 32556650, 1650306352, 100688420034, 7262453789300, 609263939139482, 58684327404118440, 6419194423681262210, 790005709370352467020, 108514436287885023435930, 16520198768574933272377952, 2770418328864442110268310402, 508995643667831746279224633828

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..160

Formula

E.g.f.: Sum_{n>=0} (2*x)^n * exp(n^2*x) / (1 + x*exp(n*x))^(n+1).

Example

E.g.f.: A(x) = 1 + x + 6*x^2/2! + 60*x^3/3! + 1040*x^4/4! + 24650*x^5/5! +...
where the e.g.f. satisfies following series identity:
A(x) = 1 + x*(2*exp(x)-1) + x^2*(2*exp(2*x)-1)^2 + x^3*(2*exp(3*x)-1)^3 + x^4*(2*exp(4*x)-1)^4 + x^5*(2*exp(5*x)-1)^5 + x^6*(2*exp(6*x)-1)^6 +...
A(x) = 1/(1+x) + (2*x)*exp(x)/(1+x*exp(x))^2 + (2*x)^2*exp(4*x)/(1+x*exp(2*x))^3 + (2*x)^3*exp(9*x)/(1+x*exp(3*x))^4 + (2*x)^4*exp(16*x)/(1+x*exp(4*x))^5 + (2*x)^5*exp(25*x)/(1+x*exp(5*x))^6 + (2*x)^6*exp(36*x)/(1+x*exp(6*x))^7 +...

Prog

(PARI) {a(n)=local(A=1); A=sum(k=0, n, x^k * (2*exp(k*x +x*O(x^n)) - 1)^k); n!*polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))
(PARI) {a(n)=local(A=1); A=sum(k=0, n, (2*x)^k * exp(k^2*x +x*O(x^n)) / (1 + x*exp(k*x +x*O(x^n)))^(k+1) ); n!*polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A193421, A248615, A248653, A248654.

Sequence in context: A308332 A126574 A061573 * A092356 A353196 A285955

Adjacent sequences: A248652 A248653 A248654 * A248656 A248657 A248658

Keyword

nonn

Author

Paul D. Hanna, Oct 26 2014

Status

approved