OFFSET
0,3
COMMENTS
Stirling transform of A001405.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..550
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Stirling Transform
FORMULA
E.g.f.: BesselI(0,2*(exp(x) - 1)) + BesselI(1,2*(exp(x) - 1)).
a(n) = Sum_{k=0..n} Stirling2(n,k)*binomial(k,floor(k/2)).
MAPLE
a:= n-> add(binomial(j, floor(j/2))*Stirling2(n, j), j=0..n):
seq(a(n), n=0..30); # Alois P. Heinz, Jun 21 2018
MATHEMATICA
nmax = 24; CoefficientList[Series[Sum[Binomial[k, Floor[k/2]] x^k/Product[1 - j x, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 24; CoefficientList[Series[BesselI[0, 2 (Exp[x] - 1)] + BesselI[1, 2 (Exp[x] - 1)], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS2[n, k] Binomial[k, Floor[k/2]], {k, 0, n}], {n, 0, 24}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 21 2018
STATUS
approved