A209519 Expansion A(x) = Sum_{n>0} a(n)*x^n/(3^(n-1)*n!), A(x) satisfies A(A(A(x)))=e^x-1.

1, 1, 0, 0, 2, -21, 138, 150, -22833, 303975, 3451320, -214016553, 666006714, 228865308144, -4943013567642, -396567325158381, 21423378444873687, 1022158819761317838, -121532275123709160942

Offset

1,5

Links

Seiichi Manyama, Table of n, a(n) for n = 1..200

Formula

a(n)=3^(n-1)*n!*T(n,1), T(n,m)=1/3*(stirling2(n,m)*m!/n!-sum(k=m+1..n-1, T(k,m)*sum(i=k..n, T(n,i)*T(i,k)))-T(m,m)*sum(i=m+1..n-1, T(n,i)*T(i,m))), n>m, T(n,n)=1.

Prog

(Maxima)
T(n, m):=if n=m then 1 else 1/3*(stirling2(n, m)*m!/n!-sum(T(k, m)*sum(T(n, i)*T(i, k), i, k, n), k, m+1, n-1)-T(m, m)*sum(T(n, i)*T(i, m), i, m+1, n-1));
makelist(n!*3^(n-1)*(T(n, 1)), n, 1, 7);

Crossrefs

Cf. A184011.

Sequence in context: A171009 A098661 A095262 * A377859 A215710 A112673

Adjacent sequences: A209516 A209517 A209518 * A209520 A209521 A209522

Keyword

sign

Author

Vladimir Kruchinin, Mar 10 2012

Status

approved