A187666 Binomial convolution of the (signless) central Lah numbers (A187535) and the (signless) central Stirling numbers of the first kind (A187646).

1, 3, 51, 1599, 74545, 4654255, 365549495, 34642467783, 3846064986001, 489429448820811, 70208261310969435, 11205444535728231855, 1969021774778391995761, 377672618542009829524551, 78507169034687468202172591

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * Lah(2k,k) * Stirling1(2n-2k,n-k).

Maple

L := n -> if n=0 then 1 else binomial(2*n-1, n-1)*(2*n)!/n! fi;
seq(sum(binomial(n, k)*L(k)*abs(combinat[stirling1](2*(n-k), n-k)), k=0..n), n=0..12);

Mathematica

L[n_] := If[n == 0, 1, Binomial[2n - 1, n - 1](2n)!/n!]
Table[Sum[Binomial[n, k]L[k]Abs[StirlingS1[2n - 2k, n - k]], {k, 0, n}], {n, 0, 14}]

Prog

(Maxima) L(n):= if n=0 then 1 else binomial(2*n-1, n-1)*(2*n)!/n!;
makelist(sum(binomial(n, k)*L(k)*abs(stirling1(2*n-2*k, n-k)), k, 0, n), n, 0, 12);

Crossrefs

Cf. A187535, A187646.

Sequence in context: A126685 A355797 A246693 * A172434 A210676 A105639

Adjacent sequences: A187663 A187664 A187665 * A187667 A187668 A187669

Keyword

nonn,easy

Author

Emanuele Munarini, Mar 12 2011

Status

approved