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A176488 Triangle T(n,k) = A008292(n+1,k+1) + A176487(n,k) - 1, 0<=k<=n. 2
1, 1, 1, 1, 8, 1, 1, 23, 23, 1, 1, 54, 136, 54, 1, 1, 117, 612, 612, 117, 1, 1, 244, 2395, 4850, 2395, 244, 1, 1, 499, 8605, 31271, 31271, 8605, 499, 1, 1, 1010, 29242, 176522, 312448, 176522, 29242, 1010, 1, 1, 2033, 95714, 910466, 2620832, 2620832, 910466 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are 1, 2, 10, 48, 246, 1460, 10130, 80752, 725998, 7258092, 79834602,....

Apparently the row sums obey (-45*n+124)*s(n) +(45*n^2+127*n-654)*s(n-1) +(-206*n^2+227*n+708)*s(n-2) +(303*n^2-869*n+458)*s(n-3) -2*(71*n-125)*(n-2)*s(n-4)=0. - R. J. Mathar, Jun 16 2015

LINKS

Table of n, a(n) for n=0..51.

EXAMPLE

1;

1, 1;

1, 8, 1;

1, 23, 23, 1;

1, 54, 136, 54, 1;

1, 117, 612, 612, 117, 1;

1, 244, 2395, 4850, 2395, 244, 1;

1, 499, 8605, 31271, 31271, 8605, 499, 1;

1, 1010, 29242, 176522, 312448, 176522, 29242, 1010, 1;

1, 2033, 95714, 910466, 2620832, 2620832, 910466, 95714, 2033, 1;

1, 4080, 305317, 4407094, 19476436, 31448746, 19476436, 4407094, 305317, 4080, 1;

MAPLE

A176488 := proc(n, k)

    A008292(n+1, k+1)+A176487(n, k)-1 ;

end proc: # R. J. Mathar, Jun 16 2015

MATHEMATICA

<< DiscreteMath`Combinatorica`;

t[n_, m_, 0] := Binomial[n, m];

t[n_, m_, 1] := Eulerian[1 + n, m];

t[n_, m_, q_] := t[n, m, q] = t[n, m, q - 1] + t[n, m, q - 2] - 1;

Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}]

CROSSREFS

Cf. A007318, A008292.

Sequence in context: A166340 A157178 A174303 * A144436 A167034 A155452

Adjacent sequences:  A176485 A176486 A176487 * A176489 A176490 A176491

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Apr 19 2010

STATUS

approved

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Last modified May 12 09:53 EDT 2021. Contains 343821 sequences. (Running on oeis4.)