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A350771
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Triangle read by rows: T(n, k) = (2^(n-k-1) + 2^k - 2)*binomial(n-1, k), 0 <= k <= n-1.
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2
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0, 1, 1, 3, 4, 3, 7, 12, 12, 7, 15, 32, 36, 32, 15, 31, 80, 100, 100, 80, 31, 63, 192, 270, 280, 270, 192, 63, 127, 448, 714, 770, 770, 714, 448, 127, 255, 1024, 1848, 2128, 2100, 2128, 1848, 1024, 255, 511, 2304, 4680, 5880, 5796, 5796, 5880, 4680, 2304, 511, 1023, 5120, 11610, 16080, 16380, 15624, 16380, 16080, 11610, 5120, 1023
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OFFSET
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1,4
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COMMENTS
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The elements in T(n,k) result from the product of each element of A350770(n,k) and binomial(n-1,k).
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LINKS
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FORMULA
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T(n, k) = (2^(n-k-1) + 2^k - 2)*binomial(n-1, k).
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EXAMPLE
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Triangle begins:
0;
1, 1;
3, 4, 3;
7, 12, 12, 7;
15, 32, 36, 32, 15;
31, 80, 100, 100, 80, 31;
63, 192, 270, 280, 270, 192, 63;
127, 448, 714, 770, 770, 714, 448, 127;
255, 1024, 1848, 2128, 2100, 2128, 1848, 1024, 255;
511, 2304, 4680, 5880, 5796, 5796, 5880, 4680, 2304, 511;
1023, 5120, 11610, 16080, 16380, 15624, 16380, 16080, 11610, 5120, 1023;
...
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MAPLE
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T := n -> local k; seq((2^(n - k - 1) + 2^k - 2)*binomial(n - 1, k), k = 0 .. n - 1);
seq(T(n), n = 1 .. 11);
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PROG
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(PARI) T(n, k) = (2^(n-k-1) + 2^k - 2)*binomial(n-1, k) \\ Andrew Howroyd, Jan 05 2024
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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