A383232 Expansion of e.g.f. f(x)^2 * log(f(x)), where f(x) = 1/(1 - 5*x)^(1/5).

0, 1, 9, 122, 2242, 52180, 1471692, 48790608, 1859539344, 80109265824, 3849497255520, 204138860091264, 11842095171021696, 745962168915065088, 50708105952635996928, 3699802551156676392960, 288399758863879774476288, 23919432333548949807869952, 2103184085769044913951461376

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = Sum_{k=1..n} k * 2^(k-1) * 5^(n-k) * |Stirling1(n,k)|.

a(n) = 5^(n-1) * n! * Sum_{k=0..n-1} (-1)^k * binomial(-2/5,k)/(n-k).

a(n) = (10*n-11) * a(n-1) - (5*n-8)^2 * a(n-2) for n > 1.

Prog

(PARI) a(n) = sum(k=1, n, k*2^(k-1)*5^(n-k)*abs(stirling(n, k, 1)));

Crossrefs

Cf. A383231, A383233, A383234.

Sequence in context: A087584 A199139 A365848 * A295095 A295549 A211101

Adjacent sequences: A383229 A383230 A383231 * A383233 A383234 A383235

Keyword

nonn

Author

Seiichi Manyama, Apr 20 2025

Status

approved