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A357668 Expansion of e.g.f. sinh( 3 * (exp(x) - 1) )/3. 2
0, 1, 1, 10, 55, 307, 2026, 14779, 114157, 933616, 8110261, 74525167, 719925328, 7279859485, 76855303981, 845280487018, 9663800287483, 114601481983855, 1407040763488354, 17856103120048783, 233883061849700137, 3157648445216335528, 43887908697233605489 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
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
Sequence in context: A169720 A024210 A253002 * A316109 A188168 A199413
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 08 2022
STATUS
approved

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Last modified April 19 08:08 EDT 2024. Contains 371782 sequences. (Running on oeis4.)