A097341
a(n) = Sum_{k=0..floor(n/2)} Stirling2(n-k,k) * 2^k.
Original entry on oeis.org
1, 0, 2, 2, 6, 14, 38, 110, 342, 1134, 3990, 14830, 58006, 237998, 1021462, 4574318, 21325462, 103287598, 518768406, 2697426926, 14498316182, 80440333998, 460112203798, 2710038058862, 16418576767126, 102212840258094, 653247225514262, 4282249051881198
Offset: 0
-
my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, 2^k*x^(2*k)/prod(j=1, k, 1-j*x))) \\ Seiichi Manyama, Apr 09 2022
-
a(n) = sum(k=0, n\2, 2^k*stirling(n-k, k, 2)); \\ Seiichi Manyama, Apr 09 2022
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));
A119430
Expansion of Sum_{k>=0} 2^k*x^(2k)/Product_{j=1..k} (1 - j*2x).
Original entry on oeis.org
1, 0, 2, 4, 12, 40, 152, 640, 2928, 14400, 75744, 424640, 2527552, 15902848, 105313408, 731376640, 5311088896, 40233525248, 317296341504, 2600091120640, 22099119279104, 194487001540608, 1769555559897088, 16622286300921856
Offset: 0
-
a[n_] := Sum[2^(n-k) * StirlingS2[n - k, k], {k, 0, Floor[n/2]}]; Array[a, 25, 0] (* Amiram Eldar, Apr 09 2022 *)
-
a(n) = sum(k=0, n\2, 2^(n-k)*stirling(n-k, k, 2)); \\ Seiichi Manyama, Apr 08 2022
A353288
a(n) = Sum_{k=0..floor(n/2)} k^(n-2*k) * Stirling2(n-k,k).
Original entry on oeis.org
1, 0, 1, 1, 2, 7, 30, 139, 723, 4487, 33551, 289854, 2774999, 29016343, 333139222, 4232908176, 59442337179, 912948755487, 15154215501815, 269933506466203, 5150440487875190, 105326085645729766, 2307425141636199329, 53998118146846356916, 1343998910355295080556
Offset: 0
-
my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(2*k)/prod(j=1, k, 1-k*j*x)))
-
a(n) = sum(k=0, n\2, k^(n-2*k)*stirling(n-k, k, 2));
Showing 1-4 of 4 results.