A357736 Expansion of e.g.f. sin( sqrt(2) * (exp(x) - 1) )/sqrt(2).

0, 1, 1, -1, -11, -45, -119, -49, 2045, 18075, 105121, 436471, 679669, -10538333, -155858247, -1404609569, -9667430739, -46708291093, -25694453615, 3002522206471, 49051481154341, 546022210068595, 4800733688293929, 31399017314213487, 75507020603213405

Offset

0,5

Links

Table of n, a(n) for n=0..24.

Eric Weisstein's MathWorld, Bell Polynomial.

Formula

a(n) = Sum_{k=0..floor((n-1)/2)} (-2)^(k) * Stirling2(n,2*k+1).

a(n) = 0; a(n) = Sum_{k=0..n-1} binomial(n-1, k) * A357725(k).

a(n) = ( Bell_n(sqrt(2) * i) - Bell_n(-sqrt(2) * i) )/(2 * sqrt(2) * i), where Bell_n(x) is n-th Bell polynomial and i is the imaginary unit.

Prog

(PARI) my(N=30, x='x+O('x^N)); concat(0, apply(round, Vec(serlaplace(sin(sqrt(2)*(exp(x)-1))/sqrt(2)))))
(PARI) a(n) = sum(k=0, (n-1)\2, (-2)^k*stirling(n, 2*k+1, 2));
(PARI) Bell_poly(n, x) = exp(-x)*suminf(k=0, k^n*x^k/k!);
a(n) = round((Bell_poly(n, sqrt(2)*I)-Bell_poly(n, -sqrt(2)*I))/(2*sqrt(2)*I));

Crossrefs

Cf. A264037, A357725.

Sequence in context: A022280 A154106 A232613 * A057813 A051740 A370534

Adjacent sequences: A357733 A357734 A357735 * A357737 A357738 A357739

Keyword

sign

Author

Seiichi Manyama, Oct 11 2022

Status

approved