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A320964 a(n) = Sum_{j=0..n} Sum_{k=0..j} Stirling2(j - k, k). 2
1, 1, 2, 3, 5, 9, 18, 40, 98, 262, 757, 2344, 7723, 26918, 98790, 380361, 1531699, 6434386, 28130891, 127729731, 601196429, 2928369918, 14738842362, 76547694742, 409718539682, 2257459567237, 12789959138944, 74439150889081, 444647798089246, 2723583835351856 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The row sums of A320955 seen as a triangle are the partial sums of the antidiagonal sums of the triangle of the Stirling set numbers.

LINKS

Table of n, a(n) for n=0..29.

MAPLE

ListTools:-PartialSums([seq(add(Stirling2(n-k, k), k=0..n), n=0..29)]);

MATHEMATICA

a[n_] := Sum[Sum[StirlingS2[j - k, k], {k, 0, j}], {j, 0, n}]; Array[a, 30, 0] (* Amiram Eldar, Nov 06 2018 *)

Table[Sum[StirlingS2[j-k, k], {j, 0, n}, {k, 0, j}], {n, 0, 30}] (* Harvey P. Dale, May 15 2019 *)

PROG

(PARI) a(n)={sum(j=0, n, sum(k=0, j, abs(stirling(j-k, k, 2))))} \\ Andrew Howroyd, Nov 06 2018

CROSSREFS

Row sums of A320955 seen as a triangle.

Cf. A171367, A048993.

Sequence in context: A097332 A099236 A234535 * A130581 A051236 A003218

Adjacent sequences:  A320961 A320962 A320963 * A320965 A320966 A320967

KEYWORD

nonn

AUTHOR

Peter Luschny, Nov 06 2018

STATUS

approved

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Last modified September 24 01:21 EDT 2020. Contains 337315 sequences. (Running on oeis4.)