A136632 a(n) = Sum_{k=0..n} A136630(n,k) * 2^(nk).

1, 2, 16, 520, 66560, 33882144, 69055086592, 564152735105152, 18462508115518554112, 2418626436468567646929408, 1267795674038260517176495570944, 2658560573512321601282555747644737536

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..57

Formula

From Paul D. Hanna, Nov 25 2009: (Start)

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

a(n) = [x^n/n! ] exp(2^n*sinh(x)).

(End)

Example

From Paul D. Hanna, Nov 25 2009: (Start)
E.g.f.: A(x) = 1 + 2*x + 16*x^2/2! + 520*x^3/3! + 66560*x^4/4! +...
A(x) = 1 + sinh(2*x) + sinh(4*x)^2/2! + sinh(8*x)^3/3! + sinh(16*x)^4/4! +...+ sinh(2^n*x)^n/n! +...
a(n) = coefficient of x^n/n! in G(x)^(2^n) where G(x) = exp(sinh(x)):
G(x) = 1 + x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 12*x^5/5! + 37*x^6/6! +...+ A003724(n)*x^n/n! +... (End)

Maple

N:= 20: # to get a(0)..a(N)
E:= add(sinh(2^n*x)^n/n!, n=0..N):
S:= series(E, x, N+1):
seq(coeff(S, x, j)*j!, j=0..N); # Robert Israel, Jan 17 2018

Prog

(PARI) {a(n)=sum(k=0, n, 2^(n*k)*polcoeff(x^k/prod(j=0, k\2, 1-(2*j+k-2*(k\2))^2*x^2 +x*O(x^n)), n))}
(PARI) {a(n)=n!*polcoeff(sum(k=0, n, sinh(2^k*x +x*O(x^n))^k/k!), n)} \\ Paul D. Hanna, Nov 25 2009
(PARI) {a(n)=n!*polcoeff(exp(2^n*sinh(x +x*O(x^n))), n)} \\ Paul D. Hanna, Nov 25 2009

Crossrefs

Cf. A136630, A003724 (row sums of A136630).

Cf. A003724 (exp(sinh x)). [From Paul D. Hanna, Nov 25 2009]

Sequence in context: A063391 A002416 A013028 * A168405 A012919 A012914

Adjacent sequences: A136629 A136630 A136631 * A136633 A136634 A136635

Keyword

nonn

Author

Paul D. Hanna, Jan 14 2008

Status

approved