A386829
a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(2*n+1,k) * binomial(2*n-k,n-k).
Original entry on oeis.org
1, 13, 204, 3457, 61006, 1103598, 20299434, 377871297, 7097430726, 134243202358, 2553356761264, 48788507855562, 935791802540596, 18007015501848568, 347459946354962694, 6720599552926105377, 130263082422599127366, 2529516572366126192478
Offset: 0
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a(n) = sum(k=0, n, 3^k*2^(n-k)*binomial(2*n+1, k)*binomial(2*n-k, n-k));
A386831
a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(4*n+1,k) * binomial(4*n-k,n-k).
Original entry on oeis.org
1, 23, 814, 32102, 1330436, 56734023, 2464566064, 108464237352, 4819668737436, 215760575713148, 9716002818365314, 439628651114930102, 19971546503835844436, 910318041046245082898, 41611957337801849102064, 1906855257451887625497852, 87569968895543824193201436
Offset: 0
-
a(n) = sum(k=0, n, 3^k*2^(n-k)*binomial(4*n+1, k)*binomial(4*n-k, n-k));
A386899
a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(3*n+1,k) * binomial(2*n-k,n-k).
Original entry on oeis.org
1, 16, 339, 7840, 189295, 4689216, 118155156, 3013479744, 77557234095, 2010176842960, 52394920516939, 1371957494204544, 36062378503314436, 950984592573500800, 25147592297769065400, 666594977732384307840, 17706778517771676847215, 471217399398861925667760
Offset: 0
-
a(n) = sum(k=0, n, 3^k*2^(n-k)*binomial(3*n+1, k)*binomial(2*n-k, n-k));
A386900
a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(3*n+1,k).
Original entry on oeis.org
1, 14, 235, 4178, 76495, 1426184, 26922076, 512838410, 9837067951, 189729498350, 3675700225435, 71474375851640, 1394164222173700, 27266825345422352, 534510606516137920, 10499123975453808698, 206595710100771337327, 4071693103719194746250
Offset: 0
-
Table[Sum[3^k*2^(n-k)*Binomial[3*n+1, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Aug 07 2025 *)
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a(n) = sum(k=0, n, 3^k*2^(n-k)*binomial(3*n+1, k));
Showing 1-4 of 4 results.