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A215078 Array of sums of the first k n-th powers multiplied by binomial(n,k), read by rows. 3
0, 0, 1, 0, 2, 5, 0, 3, 27, 36, 0, 4, 102, 392, 354, 0, 5, 330, 2760, 6500, 4425, 0, 6, 975, 15880, 73350, 123090, 67171, 0, 7, 2709, 81060, 654500, 2033325, 2637327, 1200304, 0, 8, 7196, 381808, 5064780, 25926824, 59992660, 63259168, 24684612, 0, 9, 18468, 1696464, 35574840, 281668590, 1034305524, 1896003648, 1681960464, 574304985, 0, 10, 46125, 7208880, 232816500, 2740317300, 14981494710, 42457884000, 64240088580, 49143419250, 14914341925 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

If one starts the sum at j=0, the initial term T(0,0) is 1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

T(n,k) = binomial(n,k)*sum(j^n, j=1..k)

MATHEMATICA

Flatten[Table[Table[Sum[j^n, {j, 1, k}]*Binomial[n, k], {k, 0, n}], {n, 0, 10}], 1]

CROSSREFS

Binomial convolution of A215083.

Row sums are A215077

Sequence in context: A208476 A247449 A112695 * A067881 A307649 A024714

Adjacent sequences:  A215075 A215076 A215077 * A215079 A215080 A215081

KEYWORD

nonn,tabl

AUTHOR

Olivier Gérard, Aug 02 2012

STATUS

approved

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Last modified November 13 00:25 EST 2019. Contains 329083 sequences. (Running on oeis4.)