A189420 Expansion of e.g.f. exp(sin(x)+sin(x)^2).

1, 1, 3, 6, 13, 12, -121, -896, -4391, -10160, 64491, 900768, 6118693, 16033344, -198382609, -3101259776, -22263439439, -23508393728, 1747001723475, 24367272291840, 145393520219965

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Formula

a(n) = sum(m=1..n, sum(k=m..n, (binomial(m,k-m)*((-1)^(n-k)+1)*sum(i=0..k/2, (2*i-k)^n*binomial(k,i)*(-1)^((n+k)/2-i)))/2^k)/m!).

Mathematica

With[{nn=20}, CoefficientList[Series[Exp[Sin[x]+Sin[x]^2], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 01 2017 *)

Prog

(Maxima)
a(n):=sum(sum((binomial(m, k-m)*((-1)^(n-k)+1)*sum((2*i-k)^n*binomial(k, i)*(-1)^((n+k)/2-i), i, 0, k/2))/2^k, k, m, n)/m!, m, 1, n);

Crossrefs

Sequence in context: A332365 A257276 A248043 * A215972 A341249 A145604

Adjacent sequences: A189417 A189418 A189419 * A189421 A189422 A189423

Keyword

sign

Author

Vladimir Kruchinin, Apr 21 2011

Status

approved