A357667 Expansion of e.g.f. cosh( 3 * (exp(x) - 1) ).

1, 0, 9, 27, 144, 945, 6273, 44226, 339399, 2796795, 24387786, 223853355, 2159078445, 21827316888, 230536050165, 2536213188519, 28994911890048, 343806474384045, 4220933769308205, 53566838971016418, 701650841036287275, 9473067208871584407

Offset

0,3

Links

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

Eric Weisstein's World of Mathematics, Bell Polynomial.

Formula

E.g.f.: cosh( 3 * (exp(x) - 1) ).

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

a(n) = ( Bell_n(3) + Bell_n(-3) )/2, where Bell_n(x) is n-th Bell polynomial.

a(n) = 1; a(n) = 9 * Sum_{k=0..n-1} binomial(n-1, k) * A357668(k).

Prog

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

Crossrefs

Column k=9 of A357681.

Cf. A024430, A065143, A264036, A357615.

Cf. A027710, A357649, A357668.

Sequence in context: A020279 A339725 A328604 * A230185 A340235 A217640

Adjacent sequences: A357664 A357665 A357666 * A357668 A357669 A357670

Keyword

nonn

Author

Seiichi Manyama, Oct 08 2022

Status

approved