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A177386
O.g.f.: Sum_{n>=0} Product_{k=1..n} sinh(k*arcsinh(2x)).
3
1, 2, 8, 48, 400, 4192, 52720, 773536, 12970016, 244625088, 5125896112, 118137655840, 2970016739552, 80883641686848, 2372035401856352, 74528583049288768, 2497667361588205632, 88932255196677684608
OFFSET
0,2
COMMENTS
Lim_{n->infinity} n!*A177386(n) / (2^n*A177385(n)) = 1. - Vaclav Kotesovec, Nov 06 2014
LINKS
FORMULA
O.g.f.: A(x) = G(arcsinh(2x)) where G(x) = e.g.f. of A177385.
a(n) ~ c * d^n * n!, where d = 2*A249748 = 2.0937983852519084822268503..., c = 0.880333778211172907563073... (constant c is same as for A177385). - Vaclav Kotesovec, Nov 06 2014
EXAMPLE
O.g.f.: A(x) = 1 + 2*x + 8*x^2 + 48*x^3 + 400*x^4 + 4192*x^5 + ...
Let G(x) be the e.g.f. of A177385:
G(x) = 1 + x + 4*x^2/2! + 37*x^3/3! + 616*x^4/4! + 16081*x^5/5! + ...
then A(x) = G(arcsinh(2x)).
PROG
(PARI) {a(n)=local(X=x+x*O(x^n), Egf); Egf=sum(m=0, n, prod(k=1, m, sinh(k*asinh(2*X)))); polcoeff(Egf, n)}
CROSSREFS
Sequence in context: A351422 A229233 A063075 * A112541 A052667 A327904
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 15 2010
STATUS
approved