A357668 Expansion of e.g.f. sinh( 3 * (exp(x) - 1) )/3.

0, 1, 1, 10, 55, 307, 2026, 14779, 114157, 933616, 8110261, 74525167, 719925328, 7279859485, 76855303981, 845280487018, 9663800287483, 114601481983855, 1407040763488354, 17856103120048783, 233883061849700137, 3157648445216335528, 43887908697233605489

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..547

Eric Weisstein's World of Mathematics, Bell Polynomial.

Formula

a(n) = Sum_{k=0..floor((n-1)/2)} 9^k * Stirling2(n,2*k+1).

a(n) = ( Bell_n(3) - Bell_n(-3) )/6, where Bell_n(x) is n-th Bell polynomial.

a(n) = 0; a(n) = Sum_{k=0..n-1} binomial(n-1, k) * A357667(k).

Prog

(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh(3*(exp(x)-1))/3)))
(PARI) a(n) = sum(k=0, (n-1)\2, 9^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, 3)-Bell_poly(n, -3)))/6;

Crossrefs

Cf. A024429, A264037, A357572, A357598.

Cf. A027710, A356572, A357667.

Sequence in context: A169720 A024210 A253002 * A316109 A188168 A199413

Adjacent sequences: A357665 A357666 A357667 * A357669 A357670 A357671

Keyword

nonn

Author

Seiichi Manyama, Oct 08 2022

Status

approved