A353256
Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (3 * j + x).
Original entry on oeis.org
1, 0, 1, 3, 19, 171, 2044, 30528, 547390, 11457237, 274198402, 7385438214, 221099038597, 7282925988615, 261763288109884, 10194190355448399, 427609812103844122, 19220373155515189149, 921621193002227307943, 46958377673245988620737
Offset: 0
-
a[n_] := Sum[3^(n-2*k) * Abs[StirlingS1[n - k, k]], {k, 0, Floor[n/2]}]; Array[a, 20, 0] (* Amiram Eldar, Apr 09 2022 *)
-
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, 3*j+x)))
-
a(n) = sum(k=0, n\2, 3^(n-2*k)*abs(stirling(n-k, k, 1)));
A353255
Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (2 * j + x).
Original entry on oeis.org
1, 0, 1, 2, 9, 54, 429, 4252, 50605, 703388, 11184597, 200247446, 3986363597, 87343744490, 2088739037209, 54134344486296, 1511446306795417, 45227224242345336, 1443916049346447913, 48989635949583331658, 1760229264304229244753, 66770472164443344587550
Offset: 0
-
a[n_] := Sum[2^(n-2*k) * Abs[StirlingS1[n - k, k]], {k, 0, Floor[n/2]}]; Array[a, 20, 0] (* Amiram Eldar, Apr 09 2022 *)
-
my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, 2*j+x)))
-
a(n) = sum(k=0, n\2, 2^(n-2*k)*abs(stirling(n-k, k, 1)));
A353258
Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (3 * j - x).
Original entry on oeis.org
1, 0, -1, -3, -17, -153, -1846, -27828, -503000, -10599873, -255143728, -6906078108, -207627211745, -6864486246225, -247526246562328, -9667515778323735, -406560434763167342, -18316445888374834635, -880110629723965618045, -44928348211160605056537
Offset: 0
-
a[n_] := Sum[(-1)^k * 3^(n - 2*k) * Abs[StirlingS1[n - k, k]], {k, 0, Floor[n/2]}]; Array[a, 20, 0] (* Amiram Eldar, Apr 09 2022 *)
-
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, 3*j-x)))
-
a(n) = sum(k=0, n\2, (-1)^k*3^(n-2*k)*abs(stirling(n-k, k, 1)));
Showing 1-3 of 3 results.