A340336 E.g.f.: Sum_{n>=0} x^n * cosh(2^n*x).

1, 1, 3, 18, 217, 4040, 100561, 3446128, 192945537, 18959667840, 2740190273281, 511238721323264, 131740528383163393, 56049890869822200832, 38684509753685569120257, 36013995749525832089671680, 43327632503775311653615534081, 78292881069164479582179348611072

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

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

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

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 18*x^3/3! + 217*x^4/4! + 4040*x^5/5! + 100561*x^6/6! + 3446128*x^7/7! + 192945537*x^8/8! + 18959667840*x^9/9! + ...
where
A(x) = cosh(x) + x*cosh(2*x) + x^2*cosh(2^2*x) + x^3*cosh(2^3*x) + x^4*cosh(2^4*x) + x^5*cosh(2^5*x) + ...
also
A(x) = 1/(1 - x) + (x^2/2!)/(1 - 2^2*x) + (x^4/4!)/(1 - 2^4*x) + (x^6/6!)/(1 - 2^6*x) + (x^8/8!)/(1 - 2^8*x) + ...

Prog

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

Crossrefs

Cf. A340335, A340337.

Sequence in context: A111841 A279233 A071605 * A222686 A274271 A195765

Adjacent sequences: A340333 A340334 A340335 * A340337 A340338 A340339

Keyword

nonn

Author

Paul D. Hanna, Jan 12 2021

Status

approved