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A357667
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Expansion of e.g.f. cosh( 3 * (exp(x) - 1) ).
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2
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1, 0, 9, 27, 144, 945, 6273, 44226, 339399, 2796795, 24387786, 223853355, 2159078445, 21827316888, 230536050165, 2536213188519, 28994911890048, 343806474384045, 4220933769308205, 53566838971016418, 701650841036287275, 9473067208871584407
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OFFSET
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0,3
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..547
Eric Weisstein's MathWorld, Bell Polynomial.
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FORMULA
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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).
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PROG
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(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;
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Oct 08 2022
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STATUS
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approved
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