A383050 - OEIS

%I #12 Apr 15 2025 08:26:05

%S 1,64,665,2037,-1316,-1148,16400,-116032,809592,-6059424,49512792,

%T -442266888,4302605280,-45351578400,515054655360,-6268075470720,

%U 81309027784320,-1118525784929280,16235659302272640,-247395991797912960,3936073920965890560,-64988868076072657920

%N a(n) = Sum_{k=0..n} (k+1)^6 * Stirling1(n,k).

%C Inverse Stirling transform of (n+1)^6.

%H Christian G. Bower, <a href="https://oeis.org/transforms_pari.txt">PARI programs for transforms</a>, 2007.

%H N. J. A. Sloane, <a href="/transforms.txt">Maple programs for transforms</a>, 2001-2020.

%F E.g.f.: Sum_{k>=0} (k+1)^6 * log(1+x)^k / k!.

%F E.g.f.: (1+x) * Sum_{k=0..6} Stirling2(7,k+1) * log(1+x)^k.

%o (PARI) a(n) = sum(k=0, n, (k+1)^6*stirling(n, k, 1));

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k+1)^6*log(1+x)^k/k!)))

%Y Column k=6 of A383049.

%K sign

%O 0,2

%A _Seiichi Manyama_, Apr 14 2025