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)));
A353257
Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (2 * j - x).
Original entry on oeis.org
1, 0, -1, -2, -7, -42, -341, -3452, -41835, -590452, -9511213, -172182182, -3460540075, -76455710870, -1841772619273, -48043721545240, -1349168210580087, -40581475067022120, -1301688751836211065, -44352720153871514858, -1599833618118922360175
Offset: 0
-
a[n_] := Sum[(-1)^k * 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, (-1)^k*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)));
A353262
Expansion of Sum_{k>=0} x^(2*k)/Product_{j=1..k} (1 - 3 * j * x).
Original entry on oeis.org
1, 0, 1, 3, 10, 36, 145, 666, 3466, 19956, 124111, 821601, 5755987, 42634089, 333827776, 2759262897, 24000288202, 218806121205, 2082848200057, 20639203885008, 212441617055458, 2268057343273491, 25085332185250564, 287096974919978292, 3395697093278589844
Offset: 0
-
a[n_] := Sum[3^(n-2*k) * StirlingS2[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^(2*k)/prod(j=1, k, 1-3*j*x)))
-
a(n) = sum(k=0, n\2, 3^(n-2*k)*stirling(n-k, k, 2));
A353290
a(n) = Sum_{k=0..floor(n/2)} (n-k)^(n-2*k) * |Stirling1(n-k,k)|.
Original entry on oeis.org
1, 0, 1, 2, 19, 393, 15177, 939394, 85063260, 10599342278, 1739073390797, 363404567436467, 94224446795779884, 29683590039199285223, 11167286542016941966714, 4945143125245884296040780, 2546112368234517215955646341, 1508197687055444623135714912377
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, k*j+x)))
-
a(n) = sum(k=0, n\2, (n-k)^(n-2*k)*abs(stirling(n-k, k, 1)));
Showing 1-5 of 5 results.