A323722 Expansion of e.g.f. log(1 + exp(x)*sinh(sqrt(2)*x)/sqrt(2)).

0, 1, 1, 1, -2, -7, 6, 119, 120, -2911, -12518, 90055, 977164, -2167375, -83354634, -168068473, 7777602768, 58283146817, -727882529102, -12779261480825, 46543629605236, 2663317412960849, 7760606919565134, -548896641490323385, -5830401238269419400, 104847450848773542497

Offset

0,5

Links

Table of n, a(n) for n=0..25.

Formula

E.g.f.: log(1 + Sum_{k>=1} Pell(k)*x^k/k!).

a(0) = 0; a(n) = Pell(n) - (1/n)*Sum_{k=1..n-1} binomial(n,k)*Pell(n-k)*k*a(k).

Maple

seq(n!*coeff(series(log(1+exp(x)*sinh(sqrt(2)*x)/sqrt(2)), x=0, 26), x, n), n=0..25); # Paolo P. Lava, Jan 29 2019

Mathematica

FullSimplify[nmax = 25; CoefficientList[Series[Log[1 + Exp[x] Sinh[Sqrt[2] x]/Sqrt[2]], {x, 0, nmax}], x] Range[0, nmax]!]
a[n_] := a[n] = Fibonacci[n, 2] - Sum[Binomial[n, k] Fibonacci[n - k, 2] k a[k], {k, 1, n - 1}]/n; a[0] = 0; Table[a[n], {n, 0, 25}]

Crossrefs

Cf. A000129, A006673, A007553, A112005, A279271.

Sequence in context: A225101 A351823 A286800 * A021365 A179378 A155541

Adjacent sequences: A323719 A323720 A323721 * A323723 A323724 A323725

Keyword

sign

Author

Ilya Gutkovskiy, Jan 25 2019

Status

approved