A356039
a(n) = Sum_{k=1..n} binomial(n,k) * sigma_3(k).
Original entry on oeis.org
1, 11, 58, 243, 866, 2804, 8485, 24387, 67333, 180086, 469338, 1196976, 2996956, 7385837, 17954243, 43125267, 102494548, 241309031, 563341508, 1305142418, 3002938045, 6866090880, 15609292379, 35299794600, 79443050541, 177989130174, 397124963671, 882642816697, 1954708794400
Offset: 1
-
with(numtheory): seq(add(sigma[3](i)*binomial(n,i), i=1..n), n=1..60); # Ridouane Oudra, Oct 31 2022
-
Table[Sum[Binomial[n, k] * DivisorSigma[3, k], {k, 1, n}], {n, 1, 40}]
-
a(n) = sum(k=1, n, binomial(n,k) * sigma(k, 3)); \\ Michel Marcus, Jul 24 2022
A356338
a(n) = Sum_{k=1..n} binomial(2*n, n-k) * sigma(k).
Original entry on oeis.org
1, 7, 37, 179, 826, 3703, 16283, 70619, 303121, 1290682, 5460511, 22981019, 96296552, 402024497, 1673116072, 6944105579, 28752345362, 118801061059, 489959398840, 2017339105514, 8293732341134, 34051489445365, 139634028015269, 571955737066307, 2340402722605976, 9567794393004816
Offset: 1
-
Table[Sum[Binomial[2*n, n-k]*DivisorSigma[1, k], {k, 1, n}], {n, 1, 30}]
-
a(n) = sum(k=1, n, binomial(2*n, n-k) * sigma(k)); \\ Michel Marcus, Aug 05 2022
A356341
a(n) = Sum_{k=1..n} binomial(2*n, k) * sigma(k).
Original entry on oeis.org
2, 22, 131, 806, 3607, 20395, 84254, 422230, 1842359, 8616007, 33843614, 173724659, 676938316, 2983855666, 12806013721, 57981927158, 223432922515, 1040923729567, 4004885305320, 18277809794671, 75668287229078, 317458937099194, 1215454524390767, 5785782106653667
Offset: 1
-
Table[Sum[Binomial[2*n, k]*DivisorSigma[1, k], {k, 1, n}], {n, 1, 30}]
-
a(n) = sum(k=1, n, binomial(2*n, k) * sigma(k)); \\ Michel Marcus, Aug 05 2022
A356344
a(n) = Sum_{k=1..n} binomial(2*k, k) * sigma(k).
Original entry on oeis.org
2, 20, 100, 590, 2102, 13190, 40646, 233696, 865756, 4191364, 12656548, 88372916, 233981316, 1196779716, 4919600196, 23553092286, 65558004246, 419488280946, 1126393556946, 6915947767386, 24140199749466, 99887762443386, 297490099905786, 2232346320891786, 6151075120462098
Offset: 1
-
Table[Sum[Binomial[2*k, k]*DivisorSigma[1, k], {k, 1, n}], {n, 1, 30}]
-
a(n) = sum(k=1, n, binomial(2*k, k) * sigma(k)); \\ Michel Marcus, Aug 05 2022
Comments