A091345 Exponential convolution of A069321(n) with itself, where we set A069321(0)=0.

0, 0, 2, 30, 398, 5430, 79022, 1238790, 20944478, 381167670, 7443745742, 155454939750, 3459933837758, 81801569650710, 2048133412585262, 54153668865539910, 1508122968767710238, 44130728380569410550

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n)=Sum(C(n, k)Sum(i!i Stirling2(k, i), i=1, .., k)Sum(i!i Stirling2(n-k, i), i=1, .., n-k), k=0, .., n)

E.g.f.: (exp(x)-1)^2 / (2-exp(x))^4. - Vaclav Kotesovec, May 07 2019

a(n) ~ n! * n^3 / (96 * log(2)^(n+4)). - Vaclav Kotesovec, May 07 2019

Mathematica

Table[ Sum[Binomial[n, k]Sum[i!i StirlingS2[k, i], {i, 1, k}]Sum[i!i StirlingS2[n - k, i], {i, 1, n - k}], {k, 0, n}], {n, 0, 20}]
nmax = 20; CoefficientList[Series[(E^x-1)^2 / (2-E^x)^4, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, May 07 2019 *)

Crossrefs

Sequence in context: A216119 A083446 A230726 * A147682 A211906 A077517

Adjacent sequences: A091342 A091343 A091344 * A091346 A091347 A091348

Keyword

easy,nonn

Author

Mario Catalani (mario.catalani(AT)unito.it), Jan 01 2004

Status

approved