A233395 E.g.f.: Sum_{n>=0} ( Sum_{k=1..n} x^k/k )^n / n!.

1, 1, 1, 4, 10, 46, 236, 1422, 8856, 68868, 592164, 5421384, 54606168, 599176800, 7035165528, 89675702976, 1220188038816, 17545121203296, 266689148404032, 4300256707369056, 73151041156483104, 1307045473317495360, 24472776142475956800, 479965450319937538560, 9829149455867331588480

Offset

0,4

Comments

Compare to: 1/(1-x) = Sum_{n>=0} ( Sum_{k>=1} x^k/k )^n / n!.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..290

Example

E.g.f.: A(x) = 1 + x + x^2/2! + 4*x^3/3! + 10*x^4/4! + 46*x^5/5! + 236*x^6/6! +...
where
A(x) = 1 + x + (x + x^2/2)^2/2! + (x + x^2/2 + x^3/3)^3/3! + (x + x^2/2 + x^3/3 + x^4/4)^4/4! + (x + x^2/2 + x^3/3 + x^4/4 + x^5/5)^5/5! +...

Prog

(PARI) {a(n)=n!*polcoeff(sum(m=0, n, sum(k=1, m, x^k/k +x*O(x^n))^m/m!), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A149229 A149230 A115327 * A197664 A099606 A149231

Adjacent sequences: A233392 A233393 A233394 * A233396 A233397 A233398

Keyword

nonn

Author

Paul D. Hanna, Dec 08 2013

Status

approved