A353252
Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (j + 2 * x).
Original entry on oeis.org
1, 0, 2, 2, 8, 24, 100, 488, 2832, 19096, 147296, 1281392, 12422864, 132870368, 1554525152, 19750621216, 270817685568, 3986140113792, 62686410981696, 1048946532137216, 18608550117641728, 348854564104019072, 6891109834644748032, 143058034748452036352
Offset: 0
-
a[n_] := Sum[2^k * Abs[StirlingS1[n - k, k]], {k, 0, Floor[n/2]}]; Array[a, 25, 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, j+2*x)))
-
a(n) = sum(k=0, n\2, 2^k*abs(stirling(n-k, k, 1)));
A353254
Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (j - 2 * x).
Original entry on oeis.org
1, 0, -2, -2, 0, 0, -12, -88, -608, -4664, -40032, -381200, -3993520, -45685472, -566975456, -7589393568, -109019255360, -1673050977024, -27321358963904, -473094230383616, -8659054324278528, -167044915214322816, -3387793305708038400, -72061754672510128384
Offset: 0
-
a[n_] := Sum[(-2)^k * Abs[StirlingS1[n - k, k]], {k, 0, Floor[n/2]}]; Array[a, 25, 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, j-2*x)))
-
a(n) = sum(k=0, n\2, (-2)^k*abs(stirling(n-k, k, 1)));
A352802
Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (j + 3 * x).
Original entry on oeis.org
1, 0, 3, 3, 15, 45, 198, 972, 5652, 37881, 289548, 2492640, 23906475, 253012653, 2930556024, 36883817127, 501315357690, 7318715960511, 114224260779891, 1897913866979529, 33449523840512127, 623265596538965334, 12241892922194658510, 252793167644378784006
Offset: 0
-
a[n_] := Sum[3^k * Abs[StirlingS1[n - k, k]], {k, 0, Floor[n/2]}]; Array[a, 25, 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, j+3*x)))
-
a(n) = sum(k=0, n\2, 3^k*abs(stirling(n-k, k, 1)));
A353260
Expansion of Sum_{k>=0} (-1)^k * x^(2*k)/Product_{j=1..k} (1 - j * x).
Original entry on oeis.org
1, 0, -1, -1, 0, 2, 5, 8, 6, -18, -111, -377, -953, -1567, 964, 23411, 133702, 554185, 1801323, 3910514, -2415952, -92788743, -700128734, -3842587204, -17042883146, -57693979779, -86308109341, 779904767601, 10180307035351, 78523141206142, 481780714913151
Offset: 0
-
a[n_] := Sum[(-1)^k * StirlingS2[n - k, k], {k, 0, Floor[n/2]}]; Array[a, 30, 0] (* Amiram Eldar, Apr 09 2022 *)
-
my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, (-1)^k*x^(2*k)/prod(j=1, k, 1-j*x)))
-
a(n) = sum(k=0, n\2, (-1)^k*stirling(n-k, k, 2));
Showing 1-4 of 4 results.