OFFSET
0,2
FORMULA
a(n) = Sum_{m=0..n} (-1)^m*A282629(n, m), n >= 0.
E.g.f.: exp(x)*exp(1 - exp(3*x)).
a(n) = (1/e)*Sum_{m>=0} ((-1)^m / m!)*(1 + 3*m)^n, n >= 0, (Dobiński type formula).- Wolfdieter Lang, Apr 10 2017
a(0) = 1; a(n) = a(n-1) - Sum_{k=1..n} binomial(n-1,k-1) * 3^k * a(n-k). - Ilya Gutkovskiy, Nov 29 2023
MATHEMATICA
Fold[#2 - #1 &, Reverse@ #] & /@ Table[Sum[Binomial[m, k] (-1)^(k - m) (1 + 3 k)^n/m!, {k, 0, m}], {n, 0, 19}, {m, 0, n}] (* Michael De Vlieger, Apr 08 2017 *)
PROG
(PARI) T(n, m) = sum(k=0, m, binomial(m, k) * (-1)^(k - m) * (1 + 3*k)^n/m!);
a(n) = sum(m=0, n, (-1)^m*T(n, m)); \\ Indranil Ghosh, Apr 10 2017
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Wolfdieter Lang, Apr 05 2017
STATUS
approved