A357931 a(n) = Sum_{k=0..floor(n/3)} |Stirling1(n - 2*k,n - 3*k)|.

1, 1, 1, 1, 2, 4, 7, 13, 27, 57, 120, 262, 593, 1361, 3171, 7559, 18356, 45186, 112927, 286689, 737641, 1921639, 5070154, 13540352, 36566737, 99830013, 275459693, 767798853, 2160953618, 6139721116, 17604534427, 50924095081, 148570523479, 437071675997

Offset

0,5

Links

Table of n, a(n) for n=0..33.

Formula

G.f.: Sum_{k>=0} x^k * Product_{j=0..k-1} (1 + j * x^2).

Mathematica

Table[Sum[Abs[StirlingS1[n-2k, n-3k]], {k, 0, Floor[n/3]}], {n, 0, 40}] (* Harvey P. Dale, Nov 01 2023 *)

Prog

(PARI) a(n) = sum(k=0, n\3, abs(stirling(n-2*k, n-3*k, 1)));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, 1+j*x^2)))

Crossrefs

Cf. A124380, A357932, A357933.

Cf. A353223, A357901, A357925.

Sequence in context: A265580 A136408 A317718 * A103104 A103480 A024826

Adjacent sequences: A357928 A357929 A357930 * A357932 A357933 A357934

Keyword

nonn

Author

Seiichi Manyama, Oct 21 2022

Status

approved