A340337 E.g.f.: Sum_{n>=0} x^n * sinh(2^n*x).

1, 4, 25, 224, 3201, 84672, 3806209, 236372992, 19119439873, 2286411453440, 470951855390721, 151134872556036096, 63605129403489583105, 35431710997077282635776, 31045153846201687002316801, 45105011047956365189484904448, 91364791547859831329029596643329

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Formula

E.g.f.: Sum_{n>=0} x^n * sinh(2^n*x).

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

Example

E.g.f.: A(x) = x + 4*x^2/2! + 25*x^3/3! + 224*x^4/4! + 3201*x^5/5! + 84672*x^6/6! + 3806209*x^7/7! + 236372992*x^8/8! + 19119439873*x^9/9! + ...
where
A(x) = sinh(x) + x*sinh(2*x) + x^2*sinh(2^2*x) + x^3*sinh(2^3*x) + x^4*sinh(2^4*x) + x^5*sinh(2^5*x) + ...
also
A(x) = x/(1 - 2*x) + (x^3/3!)/(1 - 2^3*x) + (x^5/5!)/(1 - 2^5*x) + (x^7/7!)/(1 - 2^7*x) + ...

Prog

(PARI) {a(n) = my(A = sum(m=0, n, x^m * sinh(2^m*x +x*O(x^n)) )); n!*polcoeff(A, n)}
for(n=1, 20, print1(a(n), ", "))
(PARI) {a(n) = my(A = sum(m=0, n\2, x^(2*m+1)/(2*m+1)! * 1/(1 - 2^(2*m+1)*x +x*O(x^n)) )); n!*polcoeff(A, n)}
for(n=1, 20, print1(a(n), ", "))

Crossrefs

Cf. A340335, A340336.

Sequence in context: A246951 A302587 A302608 * A001247 A031152 A010845

Adjacent sequences: A340334 A340335 A340336 * A340338 A340339 A340340

Keyword

nonn

Author

Paul D. Hanna, Jan 12 2021

Status

approved