A346752 Expansion of e.g.f. log( 1 + x^4 * exp(x) / 4! ).

0, 0, 0, 0, 1, 5, 15, 35, 35, -504, -6090, -45870, -265155, -990275, 2733731, 113064315, 1571621870, 15859846380, 116145112140, 289646855916, -9965576133855, -255337210989315, -4024508801328785, -47031887951290165, -338016913616223534, 1717029492398463650

Offset

0,6

Links

Seiichi Manyama, Table of n, a(n) for n = 0..487

Formula

a(0) = 0; a(n) = binomial(n,4) - (1/n) * Sum_{k=1..n-1} binomial(n,k) * binomial(n-k,4) * k * a(k).

a(n) = n! * Sum_{k=1..floor(n/4)} (-1)^(k-1) * k^(n-4*k-1)/(24^k * (n-4*k)!). - Seiichi Manyama, Dec 14 2023

Mathematica

nmax = 25; CoefficientList[Series[Log[1 + x^4 Exp[x]/4!], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 0; a[n_] := a[n] = Binomial[n, 4] - (1/n) Sum[Binomial[n, k] Binomial[n - k, 4] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 25}]

Crossrefs

Cf. A000332, A009306, A145454, A346750, A346751, A346755.

Sequence in context: A083049 A015627 A156778 * A292955 A295005 A072186

Adjacent sequences: A346749 A346750 A346751 * A346753 A346754 A346755

Keyword

sign

Author

Ilya Gutkovskiy, Aug 01 2021

Status

approved