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 A357667 Expansion of e.g.f. cosh( 3 * (exp(x) - 1) ). 2
 1, 0, 9, 27, 144, 945, 6273, 44226, 339399, 2796795, 24387786, 223853355, 2159078445, 21827316888, 230536050165, 2536213188519, 28994911890048, 343806474384045, 4220933769308205, 53566838971016418, 701650841036287275, 9473067208871584407 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..547 Eric Weisstein's MathWorld, Bell Polynomial. FORMULA 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

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Last modified March 29 01:21 EDT 2023. Contains 361596 sequences. (Running on oeis4.)