A245076 E.g.f.: Sum_{n>=0} exp(n*5^n*x) * x^n/n!.

1, 1, 11, 226, 17001, 2671876, 1242300001, 1250703890626, 3363964848750001, 20117722302277734376, 302329590133667187500001, 10299774530356369019736328126, 846958190132982653045661328125001, 160085716663876329020695686381591796876

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Vaclav Kotesovec, Asymptotic of sequences A244820, A244821 and A244822

Formula

a(n) = Sum_{k=0..n} C(n,k) * k^(n-k) * 5^(k*(n-k)).

O.g.f.: Sum_{n>=0} x^n/(1 - n*5^n*x)^(n+1).

Mathematica

Flatten[{1, Table[Sum[Binomial[n, k]*k^(n-k)*5^(k*(n-k)), {k, 0, n}], {n, 1, 20}]}]

Prog

(PARI) {a(n) = sum(k=0, n, binomial(n, k) * k^(n-k) * 5^(k*(n-k)) )}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A244820, A244821, A244822.

Sequence in context: A187646 A347482 A170948 * A120850 A289716 A305141

Adjacent sequences: A245073 A245074 A245075 * A245077 A245078 A245079

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jul 11 2014

Status

approved